Velocity

17 Terminal Velocity Examples: And Problem Examples

by

Table of Contents

Definition of Terminal Velocity

Objects falling through a fluid speed up due to gravity. But, the drag force acting on the object equals the force of gravity. At this point, the net force is zero. The object falls at a constant speed. This is known as terminal velocity.

The terminal velocity depends on various factors. Mass, size, shape, and the density of the fluid it’s falling through. A formula takes all these factors into account. Plus, constants like gravitational acceleration and drag coefficient.

Some fluids have lower terminal velocities than others. Like mist and oil droplets. They’re lighter so have a lower terminal velocity than water droplets.

Factors Affecting Terminal Velocity

In understanding the physics of terminal velocity, it’s important to take into account the different factors that affect it. 

  • One key factor is the shape and size of the object. A more streamlined shape will have a lower air resistance and achieve a higher terminal velocity. 
  • Another factor is the density of the air, with denser air resulting in a lower terminal velocity. 
  • Surface area is also important, as a larger surface area creates more air resistance and lowers the terminal velocity of an object.

Below is a table illustrating further factors affecting terminal velocity:

Factor Effect
Gravity Increases terminal velocity
Air resistance Decreases terminal velocity
Object weight Heavier objects reach terminal velocity faster
Viscosity of fluid Higher viscosity results in lower terminal velocity
Height above ground Higher heights increase terminal velocity

It’s worth noting that the terminal velocity of an object can also be affected by external forces acting on it, such as wind or other forces.

To accurately calculate the terminal velocity of an object, it’s important to take into account all of the different factors that can affect it and use the appropriate equation. It’s also important to consider the units being used and to ensure they are consistent throughout the calculation.

Force Acting on the Object

Gravitational force has a huge impact on terminal velocity. The more massive the object, the more powerful the force is, resulting in faster descent. However, its surface area in contact with the air affects the force too. Bigger surface area increases air resistance and decreases terminal velocity.

Furthermore, shape of the object is also important. Objects with a streamlined shape experience less air resistance, so they fall faster than ones with an irregular shape. Additionally, environmental conditions such as atmospheric density and temperature can influence the terminal velocity.

By understanding how forces act on objects, we can control their motion better. By taking into account various factors like size, shape and environment, we can adjust our equipment to ensure a safe landing. 

Drag Force

Terminal velocity, the maximum speed an object falls through a medium such as air or water, is affected by the force of the medium, also known as Air Resistance. When an object moves through a fluid medium, it creates a wake of disturbed fluid around it. This turbulent wake is called drag force.

To understand the impact of drag force on terminal velocity, we can look at its formula: Fd = 1/2ρv2CdA. In simpler terms, the coefficient of drag (Cd) expresses the aerodynamic properties; A refers to area; and v is velocity. 

To reduce drag force, some suggestions include: 

  • Streamlining the body
  • Reducing surface area 
  • Using smooth surfaces
  • Increasing the density of an object.

Gravity

The force that pulls objects together is a major factor influencing terminal velocity. It is known as the basic force of nature and is present in every part of the natural world.

See the gravity table below to observe how planets with different gravitational forces influence terminal velocity of various objects compared to Earth.

Planet Gravity (m/s2) 
Earth 9.8
Moon 1.6
Mars 3.71
Jupiter 24.19

It’s essential to recognize that apart from variations in gravity levels, other elements such as air resistance and wind direction can also affect terminal velocity.

Some tips that may help maintain the right terminal velocity include:

  • Streamlining an object’s shape
  • Reducing surface area
  • Increasing mass to minimize air resistance.

The mass increases acceleration towards the earth’s center or the planet’s surface, allowing for a faster, safe landing without surpassing dangerous maximum speeds.

Mass and Size of the Object

Mass and size of an object have a significant role in the terminal velocity it achieves. Heavier and larger objects fall towards the earth with greater force, thus having higher terminal velocities.

Mass Size Terminal Velocity
100g Small 22.5m/s
500g Medium 50.1m/s
2kg Large 99.3m/s

To lessen the terminal velocity, the mass can be reduced or air resistance can be increased by using a parachute or other similar items. Shape is also important; streamlined shaped objects have less air resistance and can achieve higher velocities than irregular-shaped ones.

For better results, one could attach items that catch air onto the shape of the object in order to reduce the terminal velocity. However, this method is not practical for all scenarios.

Velocity of the Object

The rate at which objects fall is referred to as terminal velocity. Mass, surface area, and shape all affect the speed of this fall.

Mass The bigger the mass, the higher the terminal velocity.
Surface Area A larger surface area leads to a lower terminal velocity.
Shape Aerodynamic shapes have slower terminal velocities than non-aerodynamic shapes.

Air resistance grows with speed. Eventually, the force of air resistance equals the force of gravity, causing the object to remain at a constant speed – terminal velocity.

For objects falling in Earth’s atmosphere, such as skydivers or parachutes, air pressure and temperature can also change terminal velocity. Temperature and density differences at different altitudes can impact the fall speed.

Knowledge of terminal velocity is important to understand physics and to use it to control objects’ fall speeds or avoid potential dangers. 

Density and Viscosity of the Fluid

The density and viscosity of a fluid are key to understanding terminal velocity. Viscosity also plays a role, with higher viscosity meaning slower settling due to increased friction.

Temperature and pressure can change the fluid’s density and viscosity, thus impacting the object’s terminal velocity. Surprisingly, fluids with very low viscosities can lead to terminal velocity changes similar to those in high viscosity fluids. This is likely due to turbulence and boundary layer effects.

John Michell was the first to measure terminal velocity in 1784. His finding was a major advancement in fluid dynamics and still remains important to physics research today. 

Shape of the Object

Shape affects an object’s terminal velocity and thus, its descent. Let’s look at some examples.

A table gives us a better understanding:

Shape of the object Terminal Velocity
Round object Low resistance = high velocity.
Cylindrical-shaped Moderate resistance = moderate velocity.Higher than round-shaped objects.
Flat surface High resistance = low velocity.Lower than round or cylindrical shaped objects.

Shape is a key factor for terminal velocity.

One way to change terminal velocity is to alter the shape; either the width or height. Also, changing weight has an impact; heavier objects have higher speeds due to their mass-to-air-resistance ratio.

Calculation of Terminal Velocity

Terminal velocity is the maximum speed achieved by a falling object when the force of air resistance equals the force of gravity. Let us delve deeper into the calculation of this phenomenon.

It is essential to note that the shape of the object can affect its terminal velocity. An object with a streamlined shape will experience less air resistance and reach terminal velocity faster than a less streamlined shape.

Furthermore, let us consider a real-life example. When mist or oil droplets fall through the air, they reach their terminal velocity at much lower speeds than larger objects due to their small size and air resistance.

Formula for Terminal Velocity

Calculate the velocity at which an object can no longer accelerate by using the Terminal Velocity Formula. This formula takes into account: mass, drag coefficient, air density and cross-sectional area of the object.

Formula is given by

VT=mgρACd

Variable Description
vT Terminal Velocity (m/s)
m Mass of Object (kg)
cd Drag Coefficient (dimensionless)
A Cross Sectional Area of Object (m²)
ρ Density of Air (kg/m³)

It’s important to remember that uniform objects such as spheres or cylinders work best with the formula due to minimal irregularities in their dimensions. Also, coefficients like cd depend on the shape, texture, orientation and velocity of the object relative to the fluid it’s traveling through.

This formula is essential for fields such as skydiving, base jumping and aeronautical engineering. So, don’t miss out on opportunities or safety regulations related to these activities- knowing the Terminal Velocity Formula is key.

Expression for Terminal Velocity

Terminal Velocity is the highest velocity a body can reach when it falls, under gravity, with air resistance equal to its weight. The equation for Terminal Velocity includes: density of air, cross-section area, and the mass of the object.

Vt = (2mg)/(pACd)0.5
Where Vt is Terminal Velocity, m is mass, g is gravity, p is air density, A is the cross-section area, Cd is drag coefficient, and c is the shape constant.

Objects with a larger area or lighter in weight experience more air resistance, resulting in slower terminal velocities. This is important in aerodynamics, to understand flight patterns.

For example, a Boeing 747 airplane dropped from 30,000 feet over the Mojave desert in a test run. The crew restarted the engines and landed safely – proving that terminal velocity knowledge can be useful even in extreme conditions like high winds and temperatures.

Examples of Calculation

To illustrate various scenarios, here’s a few examples of the calculation for terminal velocity. The calculations are based on realistic physical conditions, and the scenario changes as per varying inputs.

Example Air Resistance Coefficient (c) Mass (m) kg Radius (r) m Density of Fluid (ρ) kg/m³ Terminal Velocity Vt(m/s)
1 0.23 2.5 1.26 1.22 9.91
2 .19 .89 .64 .80 6.85

Achieving Terminal Velocity

Achieving Terminal Velocity is the point at which the velocity of an object no longer increases, but remains constant. This speed is reached when the force of gravity acting on an object is equal to the force of air resistance or drag force acting in the opposite direction. The shape, size, and density of the air will determine the terminal velocity of an object.

To calculate the Terminal Velocity of an object, we can use the formula Terminal Velocity = (mass x gravity) / (drag coefficient x velocity of the object). As the object falls and reaches its Terminal Velocity, the net force acting on the object becomes zero, causing a constant speed.

A unique detail is that a smaller object will have a much lower Terminal Velocity than a larger object due to the density of the air. 

Real-life Examples of Terminal Velocity

Terminal velocity is a phenomenon where an object that falls through a fluid reaches a constant velocity due to the balance of two opposing forces: gravity and drag. Real-life examples of this phenomenon can be observed in 

  • Marble is a viscous liquid
  • Skydiver
  • Skydiver, with his arms, stretched
  • A leaf falling from trees
  • Parachute
  • Movement of feather
  • Baseball game
  • Golf-ball
  • Rainfall
  • Hailstone rain
  • Movement of the Cotton ball
  • Bullet shot
  • Piece of stick falling from a height
  • Movement of Shot-put ball
  • Game of Disc throw
  • Movement of a shot-put ball
  • Game of Cricket
  • Ball falling from a height

Terminal Velocity Example:Marble in a viscous liquid

If a marble drops into the viscous liquid, it moves down, and after a certain time, when the drag force and the downward force become equal, it gains a constant value of velocity that will be maximum during its movement. It is a terminal velocity example.

Terminal Velocity Example:Skydiver

When a skydiver jumps from a plane, after a while, we can observe that the downward force that is also considered gravity will almost have the same value as that of the drag force. It happens due to the air resistance, and the skydiver comes down with constant velocity since the acceleration will be zero.

Terminal Velocity Examples

Image Credit: Pixabay free images

Terminal Velocity Example:The skydiver with his arms stretched

The terminal velocity value will be different when the skydiver stretches his arms and legs out. The velocity will be less when he opens his arms and kegs, i.e., it may be 135 mph, and when he does not open his arms and legs, the velocity will be more, i.e., 215 mph.

Terminal Velocity Example:A leaf falling from trees

When a leaf falls from its branch due to the air movement, it moves down, and after a certain time when the drag force and the gravity become equal, it gains a constant value of velocity that will be maximum during its movement. Hence it is a terminal velocity example.

JV5YwZpX9M4u6yVXWhmNIl31nIS7qoqUd0 MZy8DJi2e9Hy6GuiGja6kCuDwUlZz3L9XGJnMwtQ7KMMGZ RKh2YK84vewRGQaN5F9LkQRu0MdNjr AmPXq0YuJ62uguOnVYq1r130Oulkk0R1Sels

Image Credit: Pixabay free images

Terminal Velocity Example:Parachute

Even when the skydiver jumps, he opens his chute. In this similar force acts on the chute. After a while, we can observe that the downward force, also considered gravity, would almost have the same value as the drag force. It happens due to the air resistance, and the skydiver comes down with constant velocity since the acceleration will be zero.

Terminal Velocity Example:Movement of feather

When a feather is plucked out from its stock and let float freely in the air, we can see that after a while, it moves down. Due to the air resistance applied to the feather, the downward force, i.e., gravity acting on the feather, will become equal to the drag force. It is a terminal velocity example.

Terminal Velocity Example:Baseball game

When you hit a ball in baseball, it travels a certain distance and drops down from that height due to gravity. During its drop at any period when the drag force and the gravity will be similar, it gains a constant value of velocity that is maximum, called terminal velocity.

Terminal Velocity Example:Golf-ball

When a golf ball is hot to a certain distance, it drops down into the hole from a certain height due to the gravity pull. During its drop at any point when the upward and downward will have equal value, terminal velocity comes into the act that has more value. Hence it is a terminal velocity example.

OrtUTKYnCkhWVEolYVrgSS1UpcvhzD8MTfgog2DV25WnAjZpOrOuZ3pwoVV2HzFDtmkbVQ2arXSvDoJsFjCfy1mcja fNR94MqYYX0QhBCPoLK wKCVH 65ylvG UC8V FQSOZZfdfz6fHne1gnq2CM

Image Credit: Pixabay free images

Terminal Velocity Example:Rainfall

When the rain falls, each droplet will have a competition to reach on earth. After a while, we can observe that the downward force, also considered gravity, will almost have the same value as the drag force. It happens due to the air resistance, and the skydiver comes down with constant velocity since the acceleration will be zero.

XZLLazFSDE5PANbH7BBjvfqAGbWaSoQRvfxPEt3jceDVMkjldxSkymx892kTIO8XsZsS8A3NjXkqBoSZLSlvhxsa2r46BOeR1iCeBAj70mRVYG9805dcJn96EUqPg JZ42vkT3b Vau8MPG3tqSIQa4

Image Credit: Pixabay free images

Terminal Velocity Example: Hailstone rain

When the hailstones fall heavily in a region, we can observe the rate at which it falls on the ground, where terminal velocity can be seen when both the upward and downward force will be the same at some point hailstone drops at constant velocity. It is a terminal velocity example.

Terminal Velocity Example: Movement of the Cotton ball

When a cotton ball is removed from its bundle and let float freely in the air, we can see that after a while, it moves down. The cotton is less dense and will have more surface area. Due to the air resistance applied to the feather, the downward force, i.e., gravity acting on the feather, will become equal to the drag force. It is a terminal velocity example.

Terminal Velocity Example: Bullet shot

In fairs and exhibitions, we observe that a playing bullet is shot upwards; if we carefully observe its movement, it reaches its maximum height and then travels down to the ground. Here we can observe the terminal velocity. Hence it is a terminal velocity example.

Terminal Velocity Example: Piece of stick falling from a height

When a piece of the stick is dropped from a certain height, it moves down due to the gravity, and after a certain time when the drag force and the gravity become equal, it gains a constant value of velocity that will be maximum during its movement. Hence it is a terminal velocity example.

Terminal Velocity Example: Game of Disc throw

When a disc is thrown at a far distance during the tournament, it drops down from a certain height due to the gravity pull. During its drop at any point of time, when the drag force that is upward force and the gravity will be similar, it gains a constant value of velocity that will be maximum during its movement. Hence it is a terminal velocity example.

hQvhV3mfZJayHwmt8qFQcc4rtWboTsvEPdkynQU XnF7uu0akuZOiSjBHgPejn3Lhd0BkjHYOLUOEHYigny3FGJvBNJCxgfk I9i9YkUnC giEUVkGKKa0F82c1nwfmChmfKDKc7mkqn5unik8 Rro8

Image Credit: Pixabay free images

Terminal Velocity Example: Movement of a shot-put ball

When a Shot-put ball is thrown at a far distance, it drops down from a certain height due to the gravity pull. During its drop at any point of time, when the drag force that is upward force and the gravity will be similar, it gains a constant value of velocity that will be maximum during its movement. Hence it is a terminal velocity example.

Terminal Velocity Example: Game of Cricket

When the batsmen hit a ball, it falls to a certain length. It falls from that height due to the air movement it moves down, and after a certain time, when the drag force that is upward force and the gravity will be similar, it gains a constant value of velocity that will be maximum during its movement. Hence it is a terminal velocity example.

Terminal Velocity Example: Ball falling from a height

When a ball is dropped from the top floor of any building; it falls from that height due to the air movement, it moves down, and after a certain time, when the drag force is upward force and the gravity are similar, it gains the constant value of velocity that will be maximum during its movement. Hence it is a terminal velocity example.

Terminal Velocity Example: Person jumping out of a plane

Assume that a person jumps from a plane. During his fall, we can notice that at some period, the upward force, called drag force, will gain a value that is almost similar to the downward force. The forces gain the same value due to air resistance that acts on the person. Here we must notice that acceleration will be zero.

The above listed are some of the major terminal velocity examples.

Importance of Terminal Velocity in Physics

Terminal velocity is a crucial concept in physics that refers to the maximum velocity that a falling object can achieve. 

  • It is important because it helps us understand the behavior of objects in motion and how varying factors such as weight, shape, and air resistance can affect their speed.
  • The terminal velocity of an object is reached when the force of air resistance acting on the object is equal to the force of gravity. The formula for calculating terminal velocity takes into account the mass and shape of the object, the viscosity of the air, and the gravitational force acting on it.
  • A key factor in determining terminal velocity is the drag coefficient, which is a measure of the resistance that an object experiences as it moves through a fluid. The shape of the object also plays a significant role in determining its terminal velocity, as objects with larger surface areas experience more air resistance and reach their terminal velocity more quickly.
  • One pro tip for understanding terminal velocity is to remember that it is proportional to the square root of the object’s weight. This means that heavier objects will have a higher terminal velocity, all other factors being equal.

Understanding terminal velocity is crucial for a wide range of applications, from designing parachutes and skydiving equipment to predicting the behavior of objects in freefall. By grasping the principles behind this important concept, we can gain a deeper understanding of the forces that govern the behavior of objects in motion.

Accounts for the Balance of Forces

Terminal velocity is key for the balance of forces on a moving object. To grasp this, let’s examine the table below:

Object Weight Surface Area Air Resistance
Ball 0.25 kg 5 cm2 Low
Feather 0.01 kg 10 cm2 High

As an object falls, gravity causes it to accelerate until it reaches terminal velocity. Here, the weight and air resistance on the object are equal, leading to a constant velocity. A feather, with its greater surface area and air resistance, will reach its terminal velocity sooner than a ball..

Explains the Behavior of Objects in Fluids

Terminal velocity is a key physics concept. It is the highest speed an object can go while free-falling in air or other fluids. Variables like size, shape and density all influence terminal velocity.

As an object falls, air resistance equals the force of gravity. This means the object can’t accelerate anymore and it falls at its terminal velocity. This concept shows how factors like weight and surface area affect objects in fluids.

Surprisingly, animals use Terminal Velocity too. Predators watch prey jump into water, as their Terminal Velocity range decreases underwater.

How can we define a terminal velocity in terms of physics?

A terminal velocity is a form of velocity that is generally observed when any material drops from a certain height.

It is also the highest value of velocity that an object gains when it passes through air or fluid. It is generally considered the total sum of upward force and downward force. Both forces tend to cancel one another, no force acts, and the value of acceleration will become zero.

Why does the name terminal velocity define it?

In physics, the velocity that acts on any material at the constant value in its vertical direction is terminal velocity.

During the fall, the upward force will be the same as the object’s weight, leading to the result of zero vertical acceleration. Here it is observed that the material reaches the ground with constant velocity. This constant vertical velocity is known to be terminal velocity.

How does the terminal velocity work?

The important terms to be considered in the working of terminal velocity are upward force, downward force, air resistance, etc.

The working of terminal velocity is nothing but considering the values of drag and downward force and how air resistance acts on the falling body.

Give one good comparison example of the values of terminal velocity?

 Numerous terminal velocity examples can give a good comparison between a feather and a ball.

The terminal velocity value is different for both feather and ball since they have different weights. The feather is so light that it takes more time to travel back to the ground than the ball. The air resistance is the reason behind this situation.

Q: How is Terminal Velocity reached?

A: Terminal Velocity is reached when the object falls at a constant speed and the force of air resistance completely balances the force of gravity.

Q: What is the formula for Terminal Velocity?

A: The formula for Terminal Velocity is v = (2mg / pAC)^(1/2), where v is the Terminal Velocity, m is the mass of the object, g is the acceleration due to gravity, p is the density of the fluid/gas, A is the projected area of the object and C is the drag coefficient of the object.

Q: How is Terminal Velocity calculated?

A: Terminal Velocity is calculated using the formula v = (2mg / pAC)^(1/2), where v is the Terminal Velocity, m is the mass of the object, g is the acceleration due to gravity, p is the density of the fluid/gas, A is the projected area of the object and C is the drag coefficient of the object.

Q: What happens when an object reaches Terminal Velocity?

A: When an object reaches Terminal Velocity, its acceleration becomes zero. This means that its velocity becomes constant.

Q: What is the typical Terminal Velocity for a human being?

A: The typical Terminal Velocity for a human being in skydiving position is about 120 mph or 193 km/h.

Q: What force acts on an object when it reaches Terminal Velocity?

A: The force acting on an object when it reaches Terminal Velocity is the force of air resistance.

Q: How do we obtain the upward force on the object?

A: We obtain the upward force on the object using the formula F = ma, where F is the force on the object, m is the mass of the object and a is the upward acceleration of the object.

Q: Is air resistance approximately proportional to the velocity of the object?

A: Yes, air resistance is approximately proportional to the velocity of the object.

Q: Since the object is zero, what happens to its acceleration when it reaches Terminal Velocity?

A: Since the object is zero, its acceleration when it reaches Terminal Velocity also becomes zero.

Q: What is the account of forces acting on an object at Terminal Velocity?

A: At Terminal Velocity, the force of gravity acting on the object is balanced by the force of air resistance acting in the opposite direction. This means that the net force acting on the object is zero.

Summary

A terminal velocity is a form of velocity that is generally observed when any material drops from a certain height. It is also referred to as the highest value of velocity that an object possesses when it makes its movements through air or fluid. Reaching terminal velocity is when the force of gravity is balanced by the force of the fluid. This gives a constant speed, known as terminal velocity. The terminal velocity will vary based on things like size, air density, and the fluid’s viscosity. The drag coefficient of an object affects its terminal velocity too: bigger objects have a lower terminal velocity; smaller objects have a higher one. Even in the same fluid, different objects can have huge differences in their terminal velocity. 

Also Read:

Mastering Velocity Measurement in Magnetohydrodynamics: A Comprehensive Guide

by
how to measure velocity in magnetohydrodynamics

Magnetohydrodynamics (MHD) is a field of study that combines the principles of fluid dynamics and electromagnetism, allowing for the investigation of the behavior of electrically conducting fluids, such as plasmas, liquid metals, and ionized gases. Accurately measuring the velocity in MHD systems is crucial for understanding and predicting the complex interactions between fluid motion and … Read more

Unveiling the Mysteries of Quantum Entanglement: A Comprehensive Guide to Measuring Velocity

by
how to measure velocity in quantum entanglement

Quantum entanglement is a fascinating and complex phenomenon that has captivated the minds of physicists and researchers worldwide. While the velocity of quantum entanglement cannot be measured directly, there are various theoretical and experimental approaches that can provide valuable insights into the dynamics and behavior of entangled systems. In this comprehensive guide, we will delve … Read more

How to Find Velocity at Impact: A Comprehensive Guide

by
how to find velocity at impact

Summary Determining the velocity at impact is a crucial aspect of understanding the dynamics of objects in free fall. This comprehensive guide will delve into the physics principles, formulas, and practical examples to help you master the art of calculating the velocity at impact. Understanding Kinematics and Free Fall Kinematics is the branch of physics … Read more

How to Find Translational Velocity: A Comprehensive Guide

by
how to find translational velocity

Translational velocity is a fundamental concept in physics that describes the rate of change in the position of an object along a linear path. Understanding how to calculate translational velocity is crucial for analyzing the motion of various systems, from point particles to rigid bodies. In this comprehensive guide, we will delve into the theoretical … Read more

Relative Velocity Between Two Objects: Detailed Analysis

by

The concept of relative velocity between two objects is a fundamental concept in physics that helps us understand how objects move in relation to each other. When two objects are in motion, their velocities are not only determined by their individual speeds but also by their relative positions and directions. In other words, the relative velocity between two objects describes the motion of one object as observed from the frame of reference of the other object. This concept is essential in various fields, including physics, engineering, and even everyday life situations. By understanding relative velocity, we can analyze and predict the motion of objects in different scenarios, such as collisions, moving vehicles, and celestial bodies. In this article, we will explore the concept of relative velocity in detail, discussing its definition, calculation methods, and practical applications. So, let’s dive in and unravel the fascinating world of relative velocity!

Key Takeaways

  • Relative velocity is the velocity of one object as observed from another object’s frame of reference.
  • The relative velocity between two objects can be calculated by subtracting the velocities of the two objects.
  • The relative velocity can be positive, negative, or zero, depending on the direction and magnitude of the velocities.
  • The concept of relative velocity is important in understanding motion in different frames of reference and solving problems involving moving objects.

Understanding Relative Velocity

Relative velocity is a fundamental concept in physics that helps us understand the motion of objects in relation to each other. It refers to the velocity of one object as observed from the frame of reference of another object. In simpler terms, it is the velocity of an object with respect to another object.

Definition and Concept

When two objects are in motion, their velocities are not only determined by their individual speeds and directions but also by their relative motion. Relative velocity takes into account the motion of both objects and provides a measure of their combined effect.

To better understand this concept, let’s consider an example. Imagine you are in a moving car, and you see a pedestrian walking on the sidewalk. The pedestrian’s velocity is relative to the car’s velocity. If the car is moving at a constant speed of 50 kilometers per hour to the east, and the pedestrian is walking at a speed of 5 kilometers per hour to the west, their relative velocity would be the difference between their velocities, which is 55 kilometers per hour to the east.

In this example, the relative velocity is calculated by considering the velocities of both the car and the pedestrian and their respective directions. This concept of relative velocity allows us to understand how objects move in relation to each other, regardless of their absolute velocities.

Calculation of Relative Velocity between Two Objects

To calculate the relative velocity between two objects, we need to consider their individual velocities and the frame of reference from which we are observing them. The relative velocity is the vector difference between the velocities of the two objects.

To calculate the relative velocity, we follow these steps:

  1. Determine the velocities of both objects. These velocities can be given as speeds and directions or as vectors with magnitudes and directions.
  2. Choose a frame of reference from which you will observe the motion of the objects. This frame of reference can be stationary or moving.
  3. Subtract the velocity of one object from the velocity of the other object. This subtraction takes into account the directions of the velocities.
  4. The result of the subtraction is the relative velocity between the two objects. It will have both magnitude and direction.

It is important to note that relative velocity is a vector quantity, meaning it has both magnitude and direction. The magnitude represents the speed at which the objects are moving relative to each other, while the direction indicates the direction of their relative motion.

By understanding and calculating relative velocity, we can analyze the motion of objects in various scenarios and gain insights into their interactions. This concept is essential in the field of kinematics, which is the branch of physics that studies the motion of objects without considering the forces causing the motion.

Relative Velocity in Same Direction

When two objects have the same speed in the same direction, their relative velocity can be determined by considering their individual velocities and the frame of reference. Relative velocity refers to the velocity of one object as observed from the perspective of another object.

In this scenario, let’s consider two cars traveling on a straight road. Car A is moving at a speed of 60 kilometers per hour (km/h), while Car B is moving at a speed of 40 km/h. Both cars are traveling in the same direction.

To calculate the relative velocity of Car B with respect to Car A, we subtract the velocity of Car A from the velocity of Car B. In this case, the relative velocity of Car B with respect to Car A would be 40 km/h – 60 km/h = –20 km/h.

The negative sign indicates that Car B is moving at a slower speed compared to Car A. It’s important to note that the negative sign is used to indicate the direction of the relative velocity, which is opposite to the direction of Car A’s motion.

In the example above, the relative velocity of Car B with respect to Car A is –20 km/h. This means that Car B is moving 20 km/h slower than Car A when both are traveling in the same direction.

To further understand relative velocity, let’s consider another example. Suppose you are walking on a moving train. If the train is moving at a speed of 50 km/h, and you are walking towards the front of the train at a speed of 5 km/h, your relative velocity with respect to the ground would be the sum of your velocity and the velocity of the train. In this case, your relative velocity with respect to the ground would be 50 km/h + 5 km/h = 55 km/h.

Relative Velocity in Different Speeds, Same Direction

When two objects have different speeds in the same direction, their relative velocity can be determined by considering the motion of one object with respect to the other. In this scenario, the objects are moving in the same direction, but at different speeds. Let’s explore how relative velocity works in this situation.

Understanding Relative Velocity

Relative velocity is the velocity of an object in relation to another object. It describes the motion of one object as observed from the frame of reference of another object. In the context of two objects moving in the same direction, relative velocity helps us understand how their speeds and directions combine.

Different Speeds, Same Direction

Consider two cars, Car A and Car B, traveling on a straight road. Car A is moving at a speed of 60 kilometers per hour, while Car B is moving at a speed of 80 kilometers per hour. Both cars are moving in the same direction.

To determine the relative velocity of Car A with respect to Car B, we subtract the velocity of Car B from the velocity of Car A. In this case, the relative velocity of Car A with respect to Car B would be 60 kilometers per hour minus 80 kilometers per hour, which equals –20 kilometers per hour.

The negative sign indicates that Car A is moving slower than Car B. It shows that Car A is falling behind Car B at a rate of 20 kilometers per hour. This negative relative velocity tells us that Car A is moving in the same direction as Car B but at a slower speed.

Visualizing Relative Velocity

To better understand the concept of relative velocity, let’s imagine a scenario where Car A is stationary, and Car B is moving at a speed of 80 kilometers per hour in the same direction. In this case, the relative velocity of Car A with respect to Car B would be 0 kilometers per hour minus 80 kilometers per hour, which equals –80 kilometers per hour.

This negative relative velocity indicates that Car A is moving in the opposite direction of Car B. It means that Car A is moving backward relative to Car B, even though Car A is actually stationary.

When two objects have different speeds in the same direction, their relative velocity can be determined by subtracting the velocity of one object from the velocity of the other. The resulting relative velocity provides insight into how the objects are moving with respect to each other. By understanding relative velocity, we can analyze the motion of objects in different scenarios and gain a deeper understanding of their interactions.

Relative Velocity in Opposite Directions

When two objects move in opposite directions, their relative velocity is determined by the difference in their individual velocities. In this scenario, the objects are moving away from each other, and their velocities have opposite signs. Let’s explore this concept further.

Understanding Relative Velocity

Relative velocity refers to the velocity of an object with respect to another object. It takes into account the motion of both objects and is measured in terms of speed and direction. To calculate relative velocity, we need to consider the velocities of both objects and their respective directions.

The Effect of Opposite Directions

When two objects move in opposite directions, their velocities have opposite signs. For example, if one object is moving with a velocity of +10 m/s and the other object is moving with a velocity of -5 m/s, their relative velocity would be the sum of their individual velocities: +10 m/s + (-5 m/s) = +5 m/s.

This means that the objects are moving away from each other at a relative velocity of 5 m/s. The positive sign indicates that the objects are moving in the same direction, while the magnitude of 5 m/s represents the speed at which they are moving away from each other.

An Example

To better understand this concept, let’s consider an example. Imagine two cars, Car A and Car B, traveling on a straight road. Car A is moving eastward with a velocity of 20 m/s, while Car B is moving westward with a velocity of 15 m/s.

To calculate the relative velocity between Car A and Car B, we subtract the velocity of Car B from the velocity of Car A: 20 m/s – 15 m/s = 5 m/s. The positive sign indicates that the cars are moving in the same direction (east-west), while the magnitude of 5 m/s represents the speed at which they are moving away from each other.

Summary

When two objects move in opposite directions, their relative velocity is determined by the difference in their individual velocities. The sign of the velocities indicates the direction of motion, while the magnitude represents the speed at which the objects are moving away from each other. Understanding relative velocity in opposite directions is essential in various fields, including kinematics and physics, as it helps us analyze the motion of objects in different frames of reference.

Relative Velocity at an Angle

When two objects are in motion, their relative velocity can be determined by considering both their speed and direction. In some cases, the objects may be moving at an angle to each other, resulting in a more complex calculation of relative velocity. In this section, we will explore how to determine the relative velocity when two objects move at an angle, using the parallelogram method and the Law of Cosines.

Relative velocity when two objects move at an angle

73uVhBsl3j9biMbGqxQA6IuraABIXZCVDMzjftSy2Z d0b87KVxv8gtQGIf sh95R2P5WprcBsc1eAFmcSGRrWUfl52VNsB2Zji5hRPU9tnj i79MQC5LndM1or9phiNLg2ikUmH 0kpfem57Q

When two objects are moving at an angle to each other, their relative velocity is the vector sum of their individual velocities. This means that we need to consider both the magnitude and direction of each object’s velocity to determine the relative velocity.

To illustrate this, let’s consider an example. Imagine two cars, Car A and Car B, moving on a straight road. Car A is traveling at a speed of 60 km/h towards the east, while Car B is moving at a speed of 40 km/h towards the north. The angle between their paths is 90 degrees.

To find the relative velocity between Car A and Car B, we can break down their velocities into their x and y components. Car A’s velocity can be represented as (60 km/h, 0 km/h), while Car B’s velocity is (0 km/h, 40 km/h). By adding these vectors together, we get the relative velocity of Car A with respect to Car B as (60 km/h, 40 km/h).

Parallelogram method and Law of Cosines

To calculate the magnitude and direction of the relative velocity when two objects move at an angle, we can use the parallelogram method or the Law of Cosines.

The parallelogram method involves constructing a parallelogram using the individual velocities of the objects. The diagonal of the parallelogram represents the relative velocity. To find the magnitude of the relative velocity, we can use the Pythagorean theorem. The direction of the relative velocity can be determined by finding the angle between the diagonal and one of the sides of the parallelogram.

The Law of Cosines can also be used to calculate the magnitude of the relative velocity. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. By applying the Law of Cosines to the triangle formed by the individual velocities and the relative velocity, we can find the magnitude of the relative velocity.

Calculation of relative velocity in different cases

The calculation of relative velocity at an angle can vary depending on the specific case. Here are a few scenarios and how to approach them:

  1. Objects moving in the same direction: If two objects are moving in the same direction, the relative velocity is the difference between their individual velocities. The direction of the relative velocity will be the same as the direction of the faster object.

  2. Objects moving in opposite directions: When two objects are moving in opposite directions, the relative velocity is the sum of their individual velocities. The direction of the relative velocity will be in the direction of the faster object.

  3. Objects moving at right angles: If two objects are moving at right angles to each other, the relative velocity can be calculated using the Pythagorean theorem. The magnitude of the relative velocity will be the square root of the sum of the squares of the individual velocities. The direction of the relative velocity can be determined using trigonometric functions.

Applications and Importance of Relative Velocity

Relative velocity is a fundamental concept in physics that plays a crucial role in various fields. Understanding the relative motion between two objects allows us to determine their velocities, measure distances, analyze fluid dynamics, and even detect the speed of rockets. Let’s explore some of the key applications and importance of relative velocity in different contexts.

Determining Velocity of Stars and Asteroids with Respect to Earth

One of the fascinating applications of relative velocity is in determining the velocity of stars and asteroids with respect to Earth. Astronomers use this concept to study celestial bodies and understand their motion in the vast expanse of space. By observing the change in position of stars or asteroids over time, scientists can calculate their relative velocities.

This information is invaluable in studying the dynamics of our universe. It helps astronomers determine the direction and speed at which stars and asteroids are moving, providing insights into their origins, interactions, and potential impact on Earth. By analyzing relative velocities, scientists can also identify objects that may pose a threat to our planet and take necessary precautions.

Measuring Distance Between Objects in Space

Another significant application of relative velocity is in measuring the distance between objects in space. Since we cannot directly measure the vast distances between celestial bodies, scientists rely on indirect methods, such as parallax and relative velocity.

Parallax involves observing the apparent shift in the position of an object when viewed from different locations. By combining parallax measurements with relative velocity calculations, astronomers can estimate the distances to stars, galaxies, and other celestial objects. This information helps us map the universe, understand its structure, and unravel the mysteries of our cosmic neighborhood.

Rocket Launch and Speed Detection

Relative velocity is also crucial in the field of rocketry. During a rocket launch, engineers need to accurately determine the speed of the rocket to ensure a successful mission. By measuring the relative velocity between the rocket and its launchpad, engineers can calculate the rocket’s speed and make necessary adjustments to achieve the desired trajectory.

Additionally, relative velocity plays a vital role in detecting the speed of rockets during their flight. By tracking the change in position of the rocket over time, scientists can calculate its velocity at any given moment. This information helps monitor the rocket’s performance, assess its efficiency, and ensure it is on the right path.

Importance in Fluid Dynamics

Relative velocity is of great importance in the field of fluid dynamics, which deals with the study of fluids in motion. Whether it’s analyzing the flow of water in a river or studying the aerodynamics of an aircraft, understanding relative velocity is essential.

In fluid dynamics, relative velocity helps determine the velocity of a fluid with respect to an object or another fluid. This information is crucial in designing efficient systems, such as pipelines, turbines, and aircraft wings. By analyzing the relative velocities of fluids, engineers can optimize the design and performance of these systems, minimizing energy loss and maximizing efficiency.

Problem Solving

In the study of relative velocity between two objects, problem-solving plays a crucial role in understanding the concepts and applying them to real-world scenarios. By solving problems, we can gain a deeper insight into the motion of objects and how they interact with each other. In this section, we will explore two example problems that will help illustrate the application of relative velocity.

Example problem 1: Finding relative velocity of a car as seen from a bus passenger

Let’s consider a scenario where a car is moving in the same direction as a bus. A passenger sitting in the bus wants to determine the relative velocity of the car with respect to the bus. To solve this problem, we need to consider the velocity of both the car and the bus.

To find the relative velocity of the car as seen from the bus passenger, we can use the concept of vector addition. We add the velocity of the car to the negative velocity of the bus to obtain the relative velocity. The negative velocity of the bus is used because the passenger is observing the car from a moving reference frame.

Let’s assume the car is moving at a speed of 60 km/h, and the bus is moving at a speed of 40 km/h. The car is moving in the same direction as the bus, so their velocities have the same sign.

To find the relative velocity, we subtract the velocity of the bus from the velocity of the car:

Relative velocity = Velocity of car – Velocity of bus

Relative velocity = 60 km/h – 40 km/h

Relative velocity = 20 km/h

Therefore, the relative velocity of the car as seen from the bus passenger is 20 km/h.

Example problem 2: Calculating the rate at which two cars approach each other

In this example problem, let’s consider two cars moving towards each other on a straight road. We want to calculate the rate at which the two cars are approaching each other.

To solve this problem, we need to consider the velocities of both cars and their directions. Let’s assume that Car A is moving towards the east with a velocity of 50 km/h, while Car B is moving towards the west with a velocity of 40 km/h.

To find the rate at which the two cars are approaching each other, we need to find the relative velocity. Since the cars are moving towards each other, their velocities have opposite signs. We can add the velocities of the two cars to obtain the relative velocity.

Relative velocity = Velocity of Car A + Velocity of Car B

Relative velocity = 50 km/h + (-40 km/h)

Relative velocity = 10 km/h

Therefore, the rate at which the two cars are approaching each other is 10 km/h.

By solving these example problems, we can see how relative velocity can be used to analyze the motion of objects in different scenarios. It allows us to understand the speed, direction, and distance between objects in motion, providing a valuable tool in the field of kinematics in physics.

In this article, we have explored the concept of relative velocity between two objects. We have learned that relative velocity refers to the velocity of one object as observed from the frame of reference of another object. It takes into account both the speed and direction of the objects.

We started by understanding the basics of motion and velocity. Motion is the change in position of an object over time, while velocity is the rate at which an object’s position changes. Velocity is a vector quantity, meaning it has both magnitude and direction.

Next, we delved into the concept of relative motion. Relative motion occurs when the motion of an object is observed from a different frame of reference. This means that the velocity of an object can vary depending on the observer’s perspective.

We discussed how to calculate relative velocity using vector addition. When two objects are moving in the same direction, we can simply subtract their velocities to find the relative velocity. However, when the objects are moving in different directions, we need to add their velocities vectorially.

Furthermore, we explored the importance of considering the frame of reference when calculating relative velocity. The frame of reference is the point from which motion is observed. Different observers in different frames of reference may perceive the motion of an object differently.

Lastly, we examined some real-life examples where the concept of relative velocity is applicable. For instance, when driving a car, the relative velocity between your car and the car in front of you determines the safe distance you need to maintain. Similarly, in sports like soccer, the relative velocity between players affects their ability to intercept the ball.

Understanding relative velocity is crucial in many fields, including physics, engineering, and transportation. It allows us to analyze the motion of objects in relation to each other and make informed decisions based on their relative speeds and directions.

Frequently Asked Questions

1. When is the relative velocity of two moving objects zero?

The relative velocity of two moving objects is zero when they are moving in the same direction with the same speed.

2. What is relative velocity?

Relative velocity refers to the velocity of an object in relation to another object. It takes into account the motion of both objects and is measured with respect to a chosen frame of reference.

3. Can the relative velocity of two bodies be negative?

Yes, the relative velocity of two bodies can be negative. It indicates that the two bodies are moving in opposite directions with respect to each other.

4. How to find the relative velocity between two objects?

yBbUHAXC59D2b7brnAhhcCof7QGL901X7ZmrTknNlU OghXsSpSdEr0NACpTSenHzWSoCJq5JQm4JH0dLfINGe1JBS1KMYerps70ppnq8ZEvOZHFPd5psVz3hMdz7l41IKUM9aPgR0CXHvPng

To find the relative velocity between two objects, subtract the velocity of one object from the velocity of the other object. The result will give you the relative velocity vector.

5. Why is relative velocity important?

Relative velocity is important because it helps us understand the motion of objects in relation to each other. It allows us to analyze the relative motion, determine the speed and direction of objects, and solve problems related to kinematics in physics.

6. What is the relative motion between two objects?

Relative motion between two objects refers to the motion of one object as observed from the perspective of another object. It takes into account the relative velocity, direction, and displacement between the two objects.

7. When is the relative velocity of two bodies maximum and minimum?

The relative velocity of two bodies is maximum when they are moving in opposite directions with the highest speed difference. It is minimum when they are moving in the same direction with the smallest speed difference.

8. Explain relative velocity between two objects moving in a plane.

When two objects are moving in a plane, their relative velocity is determined by considering their velocities as vectors. The relative velocity is the vector difference between the velocities of the two objects, taking into account their magnitudes and directions.

9. What is the relative velocity of two bodies having equal speed but moving in opposite directions?

xW6L1iWAVuwbahHd2KdXlzP6BitGHDIeG4hAOg87L37v23h1uzQt9oKWlrUEfl9gg9nov1bgusVLMvYiBYof7wildG1gEWogs8 B5RQmQlBMABiiPy4UgSKsdu8LaUOmpmgy82D5Yv1LqAWcLw
dNPvQa9yizX76KZzpvv63IA8uvYLXFbiyp8cMikvosVcQBwpxUYmKIXqgD7jpAEWIFad0Rv1gXDXfQDTKH6Rz9z4Y2qa7 h

The relative velocity of two bodies having equal speed but moving in opposite directions is twice the magnitude of their individual speeds. The direction of the relative velocity is the same as the direction of the faster object.

10. What is the relative angular velocity between two objects?

The relative angular velocity between two objects is a measure of how fast one object is rotating with respect to the other object. It is determined by the difference in their angular velocities and the distance between their rotation axes.

Also Read:

Mastering Velocity and Speed: A Comprehensive Guide for Physics Students

by
velocity and speed

Velocity and speed are fundamental concepts in physics that describe the motion of an object. While they are closely related, they are distinct quantities with different physical meanings. This comprehensive guide will delve into the technical details, formulas, examples, and numerical problems to help physics students gain a deep understanding of these essential topics. Understanding … Read more

17 Instantaneous Velocity Examples: And Problem Examples

by
quicklatex.com a273f2ac9bc064d644adb8bc6c7dd02d l3

We can calculate instantaneous velocity examples in any motion; it is defined as nothing but the length covered by the person/object at a certain point in time. There are several methods to measure the Vinst of the object considered. It can be calculated by graphical, formula, etc.

  • Speedometer devise in the car
  • Animals running to hunt
  • Typewriter
  • Arranging of coins
  • Serving food orders in a restaurant
  • Squash ball tournament
  • Musical Instruments
  • A fruit falling from a certain height of the branch
  • Waterfall
  • Elevator
  • Jiggling of balls
  • Talking
  • A person jogging with varying velocity
  • Rotating table fan
  • Train
  • Moving of jet craft
  •  Playing ball game
  • Chasing

Speedometer devise in the car

The speedometer is generally a device installed in every vehicle used to check the velocity and speeding range. The speedometer can be a perfect instantaneous velocity example. If one needs to know the velocity rate for a certain second, it can be observed in the speedometer.

Animals are running to hunt

It is common in forest areas that all the wild animals need to hunt to survive as a part of the food chain. While hunting, there will be some variation in the distance they move at different minutes. Here it will be easy for us to measure the instantaneous velocity.

Typewriter

The typewriter is one of the oldest devices to print a written document. The typing will occur at a different time and at certain distances between each word. So here, we can easily calculate the instantaneous velocity for each word.

Arranging of coins

In a mint, there will be plenty of coins. We need to organize them so that we can bundle them up nicely. We can observe how the coins move with different velocities in this process. So, it is an instantaneous velocity example.

Serving food orders in the food stall

In a crowded food stall, the food order will be based on the preparation time of the ordered food and is an instantaneous velocity example. Here, the velocity may vary for each arrangement, and we can measure the rate of velocity for a different food order.

Squash ball tournament

Squash ball is one of the international games. Here we can measure the instantaneous velocity for each move since the ball moves in a different direction and varying velocity for each hit. It is one of the prominent instantaneous velocity examples.

Musical Instruments

Various musical instruments produce different sounds when played. When we start to play a particular instrument, the different keys are pressed at different points, and even the velocity will vary. Here we can calculate the Vinst of any musical instrument.

A fruit falling from a certain height of the branch

If the fruit is fully developed or when it is a windy day, the fruit falls off the branch. While falling off, the fruits reach the ground at different velocities at a different points. Here we can find the instantaneous velocity at any point in between reaching the ground.

Waterfall

The waterfall is a very beautiful sight to watch. When the waterfalls reach the ground very fast while less speed at the top, if we desire to find the velocity at any point between the fall, then we can use Vinst. Hence, it is an actual instantaneous velocity example.

Elevator

Even an elevator is a prime instantaneous velocity example. The elevator reaches the different positions at different times; if it does not move with uniform velocity, then at any specific second or minute, we will be able to calculate the instantaneous velocity using the formula. Can measure even the Vinst of the escalator in the same way.

Jiggling of balls

The jiggling of balls is difficult and can be attained only when done thoroughly. Each ball moves at different points at varying times on different paths. If one needs to calculate the velocity at any particular position, one can use the instantaneous velocity formula. Here we can take into care the rate of velocity at various paths.

Talking

Each individual speaks with various tones; if we consider a teacher, she uses various voice modulations while teaching. Suppose one wishes to find the instantaneous velocity at any particular voice modulation. In that case, we can use position, direction, and time, and then we will be able to measure Vinst using the formula.

A person jogging with varying velocity

A person who jogs on the track reaches different distances at different times. There will be variations in his velocity while he jogs at a different position on the track. In this case, we will be able to measure the Vinst using the formula, which is the best instantaneous velocity example.

Rotating table fan

A Rotating table Fan is also a daily life instantaneous velocity example. Generally, we can vary the speed of the table fan as we need. Here, if we consider the direction and take into care of the position rate, it is possible to measure the instantaneous velocity of the rotating table fan.

Train

The train moves on the different turns and curves and keeps on changing its path at a certain rate at varying intervals, be it second or minute. So, we can find the Vinst on any path on which the train travels.

Moving of jet craft

The moving of jet craft varies its speed in different directions according to the situation. Here, take the jet craft’s location at any specific point of a minute into care that can be useful in measuring the instantaneous velocity of the moving jet craft.

Playing ball game

Playing with a ball is a fun, full game. Here we can measure the instantaneous velocity for each move since the ball moves in a different direction and varying velocity for each hit. It is one of the prominent instantaneous velocity examples.

Chasing

The chaser runs on different paths in a chasing game to catch the individuals. Here the rate of position changes frequently for every minute. If we consider the variation in time and position, we can find the instantaneous velocity.

We can observe these primary instantaneous velocity examples in this busy life.

Problems based on instantaneous velocity

To easily understand the concept of Vinst; Here are some of the problems related to measuring instantaneous velocity.

Problem 1

The movement of the tractor is given in the form of function s = t2 + 2t + 5. Measure its Instantaneous Velocity at time t = 6s.

Solution:

Here the given function of motion is s = t2 + 2t + 5.

Now we have to differentiate the above function with time, then we get

Vinst = ds / dt = d ( t2 + 2t + 5) / dt

Vinst = v(t)= 2t + 2

Given for time t = 6s, then the  Instantaneous Velocity is measured as,

V (6) = 6 (6) + 10

V (6) = 46 m/s.

Therefore, for the given function, the Instantaneous Velocity is 46 m/s.

Problem 2

Measure the instantaneous velocity at time t = 4s, given that the displacement equation is to be S = 5t3 – 2t2 + 2t + 3?

Solution:

Can solve this problem similar to the previous one; the only change to be done is given cubic should be sorted similarly as we do in the case of quadratic.

The given equation of motion is as follows

S(t) = 5t3 – 2t2 + 2t + 3. 

Vinst = ds / dt =  d ( 5t3 – 2t2 + 2t + 3) =

(3 x 5 t<sup>2 </sup>) - (2 x 2t) + 2

Vinst = 15t2– 4t + 2

Here we have to measure instantaneous velocity at t = 4s

Vinst = 14 (4)2 – 4(4) + 2

Vinst = 240 – 16 + 2

Vinst = 226 meters/second

Here Vinst is found to be 226 m/s

Problem 3

The equation of motion gives the movement of a bulldozer as S = L t2 + n, where n = 11 m and l = 8 m. In this case, measure the instantaneous velocity at t = 2s?

Solution:

 Here the equation is given as follows;

S(t) = L t2 + n

v (t) = ds / dt = 2 L t + 0

v (t) = 2 L t

Here, L = 8m   and t = 2s,

v (2) =

2 x 8 x 2

= 32 m/s.

v (t) = 32 m/s.

Here Vinst is found to be 32 m/s

Can we say that instantaneous acceleration is always normal to instantaneous velocity?

If you consider any circular motion, the acceleration of the object taken will be normal to the instantaneous velocity path, which comes under special cases such as centripetal acceleration.

Acceleration is always normal to instantaneous velocity and can be changed only in its path. The velocity will remain unchanged in some cases, and at each point, we can measure the Vinst. We can also change the trajectory according to the object’s movement.

Summary

Instantaneous velocity examples can be observed in every motion that happen around us. Vinst is defined as nothing but the length covered by the person/object at a certain point in time. in this present post we have mentioned some of the important instantaneous velocity examples.

Also Read:

How to Measure Velocity in Superconductors: A Comprehensive Guide

by
how to measure velocity in superconductors

Measuring the velocity of electrons in superconductors is a crucial aspect of understanding their transport properties and the underlying quantum mechanical phenomena. This comprehensive guide will delve into the various experimental and theoretical approaches used to determine the velocity of electrons in these remarkable materials. Fast-Pulsed Current Technique The fast-pulsed current technique is a powerful … Read more

15+ Average Velocity Examples: And Problem Examples

by
dirt bike 330815 480 1 300x200 1

This physics article will know the various average velocity examples and some problems and their different solutions.

Average velocity is the velocity that is taken into consideration when it is necessary to calculate the total displacement of the moving body by taking only its velocity at the beginning and velocity at the end and then dividing it by two. More average velocity examples can be seen daily.

Let us read the average velocity examples in detail.

Ferris wheel

The Ferris wheel is an enjoyable ride that people of all ages enjoy when visiting an amusement park. When this Ferris wheel moves, there is a change in point of position for every second, which is called velocity. Considering both starting and final velocity points, we can measure average velocity.

Metro train

Metro train is an essential transport beneficial for people working in metro cities. Here are several stations that a metro train stops at before reaching the final stop. Can measure his average velocity from the beginning; the train starts to move until it stops. t can be a good average velocity example.

Traveling on a bike

Traveling on a bike to a place will involve many different types of roads, depending on the length of the road and the displacement changes that lead to velocity changes. Then we consider measuring the average velocity of a person traveling on the bike; then, we have to consider both starting and final velocity points.

average velocity examples
 
Image Credit: Pixabay free images

Climbing on the ladder

Painters use ladders to paint the wall; while painting, they need to move to different positions at different points in time. Then we consider measuring the average velocity of a painter; then, we have to consider both starting and final velocity points. Thus we will be able to measure the Vavg of the painter’s movement.

average velocity examples
Image Credit: Pixabay free images

Moving of tractor

Plowing in a field will be easy with the help of a tractor. The plowed field will involve many different areas, depending on the length of the area and the displacement changes that lead to a change in velocity. Here we consider measuring the average velocity of a tractor; then, we have to consider both starting and final velocity points.

Athletics

If athletic competition is conducted, the athlete participating will have to cover a certain distance. It is an actual example of measuring average velocity. While running, the athletes have to run through different lengths of distance, so to know the proper velocity of the athlete, we can make use of average velocity.

Courier service

Courier services are very beneficial for quickly sending important parcels to the people. The courier services are known for their speed; the courier boy has to go to different places to deliver each item. At last, if we want to measure his Vavg, we can take the velocity at the start of his courier service, and at the end, using the formula of Vavg, we can measure the velocity courier boy.

mail truck 3248139 480
Image Credit: Pixabay free images

Paper plane

Paper plane is a fun activity that we used to play with our peer group. When we initiate the paper plane to fly, it moves to a certain distance and stops. Here if we know the initial velocity and note down the final velocity, using the formula of Vavg, we can easily find out the distance moved by the paper plane with time.

Moving of Grass-shaper

Shaping grown grass strands in a field will be easy with the help of a grass shaper. The field will involve many different strands of grasses; depending on their length, the displacement changes that lead to a change in velocity. When measuring the average velocity of a moving grass shaper, we have to consider both starting and final velocity points.

average velocity examples
Image Credit: Pixabay free images

Food delivery

Food delivery is very beneficial for the quick sending of food to the people. The food delivery apps are known for their speed in delivering food items; the delivery guy has to go to different places to deliver each item. At last, if we want to measure his Vavg, we can take the velocity at the start of his courier service and the end. Using the formula of Vavg, we can measure the velocity of the delivery guy.

average velocity examples
Image Credit: Pixabay free images

Dragging of box

Dragging a box requires strength; moving that big box from one point of position to another at a slower rate requires so much effort. If we consider both starting and final velocity points, we can measure average velocity. It is an actual average energy example.

Cat running across the streets

When a cat plays and runs across the streets, it keeps changing its path. It will be happy to see the cat enjoying. In this, we can measure the distance covered in a specific direction. Here we can find out the average velocity of the ball moved with the help of its formula and the initial and final velocities. It is a prominent average energy example.

Carom Board

When the carom pan gets hit in a carom board match, it moves to a distance. Here, we can find out the average velocity of the pan moved with the help of its formula and the initial and final velocities. It is a prominent average energy example.

average velocity examples
Image Credit: Pixabay free images

While Playing eye-spy

Playing eye-spy is ana fun game that people of all ages enjoy when they play. When the player runs to hide in this game, there is a change in point of position for every second then; it is called velocity. If we consider both starting and final velocity points, we can measure average velocity.

Cricket

When the ball gets hit in a cricket match, it moves to a far distance. For the best player, the score of batsmen is also measured on the average velocity with which the ball is hit. Here we can find out the average velocity of the ball moved with the help of its formula and the initial and final velocities. It is a prominent average energy example.

average velocity examples
Image Credit: Pixabay free images

Moving a slab

Moving a big slab is somewhat risky; moving that giant slab from one position to another at a slower rate requires so much effort. Here, if we consider both starting and final velocity points, we can measure average velocity.

The above mentioned are some important average velocity examples.

Problems based on Average Velocity

The different problems of average velocity can be solved as shown below;

Problem 1

Consider a rat travels a distance of about 5 meters to the right with the initial velocity of 4m/s and then moves towards its right to a distance of 11 meters with a final velocity of 6 m/sin with a time duration of 55 seconds. Calculate the average velocity of the movement of a rat?

Solution: First let’s note down the given data,

Vi = 4m/s

Vf = 6m/s

t = 55 seconds

The formula used to measure V is

vavg = vf – vi / t

Now substitute the given data into the formula,

Vavg = (6 – 4)/ 55

Vavg =    m/s

Therefore, the average velocity of the above-given example is  m/s.

Problem 2

Now a box is dragged to a distance of about 2 meters straight with the initial velocity of 6 m/s, and then it is moved towards the left to a distance of 5 meters with a final velocity of 8m/s in a time duration of 59 sec. Calculate the average velocity of the movement of the box?

Solution: First let’s note down the given data,

Vi = 6m/s

Vf = 8m/s

t = 59 seconds

The formula used to measure V is

vavg = vf – vi / t

Now substitute the given data into the formula,

Vavg = (8 – 6)/ 55

Vavg =    m/s

Therefore, the average velocity of the above-given example is m/s.

Frequently Asked Questions | FAQs

Can we say that velocity has direction?

Velocity is certainly a component of direction.

As we measure the velocity of anybody, material, or object, we consider the aspects of variation in displacement and time. Here if we come to displacement, then it has a direction component with the help of which we can track the path in which an object moves.

Is there any term such as negative velocity?

There is a chance that a body experiences negative velocity in many cases.

When any object is moving with a positive acceleration, the direction of that object is in the opposite path to the direction in which the acceleration is acting. In this case, we can see the negative velocity since the body travels in a negative direction.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Also Read: