How to Calculate Speed: Easy Steps With Formula And Problems

Speed is a fundamental concept in physics and everyday life. It measures how fast an object is moving and is usually expressed in units such as meters per second (m/s) or kilometers per hour (km/h). In this blog post, we will explore different methods to calculate speed, including basic formulas, advanced techniques, and special cases. So, let’s dive in and learn how to calculate speed!

The Basic Formula to Calculate Speed

how to calculate speed — Image by Fährtenleser – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 4.0.

Speed Formula in Terms of Distance and Time

The basic formula to calculate speed is straightforward: speed is equal to the distance traveled divided by the time taken. Mathematically, we can represent it as:

$speed = \frac{distance}{time}$

Here, “distance” refers to the total distance traveled, and “time” denotes the duration taken to cover that distance. For example, if a car travels 100 kilometers in 2 hours, we can calculate its speed by dividing the distance by the time:

$speed = \frac{100 \, \text{km}}{2 \, \text{h}} = 50 \, \text{km/h}$

This means that the car’s speed is 50 kilometers per hour.

Worked Out Examples Using the Basic Speed Formula

Let’s work through a couple of examples to solidify our understanding of the basic speed formula.

Example 1: A cyclist travels a distance of 40 kilometers in 2 hours. What is the cyclist’s speed?

To find the speed, we divide the distance (40 kilometers) by the time (2 hours):

$speed = \frac{40 \, \text{km}}{2 \, \text{h}} = 20 \, \text{km/h}$

Therefore, the cyclist’s speed is 20 kilometers per hour.

Example 2: A runner completes a race in 1 hour and 30 minutes, covering a distance of 21 kilometers. What is the runner’s speed?

First, we need to convert the time to hours. Since 1 hour is equal to 60 minutes, 30 minutes is equal to half an hour:

$\text{Time in hours} = 1 \, \text{hour} + \frac{30 \, \text{minutes}}{60 \, \text{minutes/hour}} = 1.5 \, \text{hours}$

Next, we can calculate the speed by dividing the distance (21 kilometers) by the time (1.5 hours):

$speed = \frac{21 \, \text{km}}{1.5 \, \text{h}} = 14 \, \text{km/h}$

Therefore, the runner’s speed is 14 kilometers per hour.

Advanced Methods to Calculate Speed

Calculating Speed with Acceleration and Time

In certain situations, an object’s speed may not remain constant. If the object undergoes acceleration (change in velocity over time), we can calculate its average speed using the following formula:

$\text{Speed} = \frac{\text{Change in velocity}}{\text{Time taken}}$

This formula measures the average speed over a specific time interval. For example, if a car accelerates uniformly from rest to a final velocity of 30 m/s over a time of 10 seconds, we can find its average speed using the acceleration formula:

$\text{Average speed} = \frac{30 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = 3 \, \text{m/s}$

Calculating Speed with Acceleration and Distance

Similarly, if we know the acceleration and the distance covered by an object, we can find its final speed using the following formula:

$\text{Speed}^2 = \text{Initial speed}^2 + 2 \times \text{Acceleration} \times \text{Distance}$

This equation is derived from the kinematic equation for motion with constant acceleration. Let’s consider an example to understand this formula better.

Example: A car accelerates uniformly from rest with an acceleration of 2 m/s^2. If it travels a distance of 100 meters, what is its final speed?

First, we need to find the speed squared:

$\text{Speed}^2 = 0^2 + 2 \times 2 \, \text{m/s}^2 \times 100 \, \text{m} = 400 \, \text{m}^2/\text{s}^2$

To find the final speed, we take the square root of 400 m^2/s^2:

$\text{Speed} = \sqrt{400 \, \text{m}^2/\text{s}^2} = 20 \, \text{m/s}$

Therefore, the car’s final speed is 20 meters per second.

Calculating Speed Using Kinetic Energy

Another interesting way to calculate an object’s speed is by using its kinetic energy. The kinetic energy of an object is given by the formula:

$\text{Kinetic Energy} = \frac{1}{2} \times \text{Mass} \times \text{Speed}^2$

We can rearrange this formula to solve for speed:

$\text{Speed} = \sqrt{\frac{2 \times \text{Kinetic Energy}}{\text{Mass}}}$

Let’s apply this formula to an example.

Example: A ball with a mass of 0.5 kg has a kinetic energy of 10 joules. What is its speed?

Plugging the values into the formula, we get:

$\text{Speed} = \sqrt{\frac{2 \times 10 \, \text{J}}{0.5 \, \text{kg}}} = \sqrt{40 \, \text{m}^2/\text{s}^2} = 2 \sqrt{10} \, \text{m/s}$

Therefore, the ball’s speed is approximately $2 \sqrt{10}$ meters per second.

Worked Out Examples Using Advanced Speed Formulas

Let’s work through a couple of examples using the advanced speed formulas we discussed.

Example 1: An object accelerates uniformly from rest and reaches a speed of 25 m/s in 5 seconds. What is its average acceleration?

To find the average acceleration, we use the formula:

$\text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time taken}}$

Substituting the given values, we have:

$\text{Acceleration} = \frac{25 \, \text{m/s} - 0 \, \text{m/s}}{5 \, \text{s}} = 5 \, \text{m/s}^2$

Therefore, the average acceleration is 5 meters per second squared.

Example 2: A car with an initial speed of 15 m/s accelerates uniformly at a rate of 2 m/s^2 for a distance of 100 meters. What is its final speed?

Using the formula:

$\text{Speed}^2 = \text{Initial speed}^2 + 2 \times \text{Acceleration} \times \text{Distance}$

we substitute the given values:

$\text{Speed}^2 = 15 \, \text{m/s}^2 + 2 \times 2 \, \text{m/s}^2 \times 100 \, \text{m} = 615 \, \text{m}^2/\text{s}^2$

Taking the square root, we find:

$\text{Speed} = \sqrt{615 \, \text{m}^2/\text{s}^2} \approx 24.8 \, \text{m/s}$

Therefore, the car’s final speed is approximately 24.8 meters per second.

Special Cases in Calculating Speed

Calculating Speed of Light and Sound

In special cases, such as the speed of light and sound, we encounter constant speeds that can be calculated directly.

The speed of light in a vacuum is a fundamental constant, denoted by the symbol “c.” Its value is approximately 299,792,458 meters per second.

The speed of sound, on the other hand, depends on various factors such as temperature and medium. In dry air at 20 degrees Celsius, the speed of sound is approximately 343 meters per second.

Calculating Speed of a Falling Object

When an object falls freely under the influence of gravity, it undergoes constant acceleration. This acceleration is denoted by “g” and is approximately 9.8 m/s^2 on the surface of the Earth.

To calculate the speed of a falling object after a certain time, we can use the formula for speed with acceleration and time:

$\text{Speed} = \text{Acceleration} \times \text{Time}$

For example, if an object falls for 3 seconds, its speed after that time would be:

$\text{Speed} = 9.8 \, \text{m/s}^2 \times 3 \, \text{s} = 29.4 \, \text{m/s}$

Calculating Speed of a Wave

In physics, the speed of a wave depends on the frequency and wavelength of the wave. The formula to calculate wave speed is:

$\text{Speed} = \text{Frequency} \times \text{Wavelength}$

For example, if a wave has a frequency of 10 Hz and a wavelength of 2 meters, its speed can be calculated as:

$\text{Speed} = 10 \, \text{Hz} \times 2 \, \text{m} = 20 \, \text{m/s}$

Worked Out Examples for Special Cases

Let’s work through a couple of examples to explore these special cases further.

Example 1: How long does it take for light from the Sun to reach Earth? (Assuming a distance of 149.6 million kilometers)

To find the time taken by light to travel from the Sun to Earth, we need to divide the distance by the speed of light:

$\text{Time} = \frac{\text{Distance}}{\text{Speed of light}} = \frac{149,600,000 \, \text{km}}{299,792,458 \, \text{m/s}}$

To convert kilometers to meters, we multiply the distance by 1000:

$\text{Time} = \frac{149,600,000 \times 1000 \, \text{m}}{299,792,458 \, \text{m/s}} = \frac{149,600,000,000 \, \text{m}}{299,792,458 \, \text{m/s}}$

Evaluating this expression, we find:

$\text{Time} \approx 499 \, \text{seconds}$

Therefore, it takes approximately 499 seconds for light from the Sun to reach Earth.

Example 2: A sound wave travels a distance of 500 meters in 2 seconds. What is its frequency?

To find the frequency of the sound wave, we divide the distance by the time:

$\text{Frequency} = \frac{\text{Distance}}{\text{Time}} = \frac{500 \, \text{m}}{2 \, \text{s}} = 250 \, \text{Hz}$

Therefore, the frequency of the sound wave is 250 Hertz.

In this blog post, we explored various methods to calculate speed. We started with the basic formula, which calculates speed in terms of distance and time. Then, we delved into more advanced techniques involving acceleration, kinetic energy, and special cases such as the speed of light, sound, falling objects, and waves. By understanding these formulas and concepts, we can accurately determine the speed of objects in different scenarios. So, the next time you find yourself needing to calculate speed, you’ll be well-equipped to do so!

Numerical Problems on how to calculate speed

A car travels a distance of 200 meters in 20 seconds. Calculate its speed.

Solution:
Given:
Distance (d) = 200 m
Time (t) = 20 s

To calculate speed, we use the formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Substituting the given values into the formula:

$\text{Speed} = \frac{200}{20} = 10 \, \text{m/s}$

Therefore, the speed of the car is 10 m/s.

An athlete runs a distance of 800 meters in 2 minutes. What is the athlete’s speed?

Solution:
Given:
Distance (d) = 800 m
Time (t) = 2 minutes = 120 seconds

To calculate speed, we use the formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Substituting the given values into the formula:

$\text{Speed} = \frac{800}{120} = 6.67 \, \text{m/s}$

Therefore, the athlete’s speed is approximately 6.67 m/s.

A train travels a distance of 500 kilometers in 5 hours. Find the speed of the train.

Solution:
Given:
Distance (d) = 500 km
Time (t) = 5 hours

To calculate speed, we use the formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Substituting the given values into the formula:

$\text{Speed} = \frac{500}{5} = 100 \, \text{km/h}$

Therefore, the speed of the train is 100 km/h.

Also Read:

TechieScience Core SME

The TechieScience Core SME Team is a group of experienced subject matter experts from diverse scientific and technical fields including Physics, Chemistry, Technology,Electronics & Electrical Engineering, Automotive, Mechanical Engineering. Our team collaborates to create high-quality, well-researched articles on a wide range of science and technology topics for the TechieScience.com website.

All Our Senior SME are having more than 7 Years of experience in the respective fields . They are either Working Industry Professionals or assocaited With different Universities. Refer Our Authors Page to get to know About our Core SMEs.

techiescience.com