17 Instantaneous Velocity Examples: And Problem Examples

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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.

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