# Why Speed and Velocity are not always equal in magnitude?

29-DEC-2017 12:16
Why Speed and Velocity are not always equal in magnitude

The speed of a body gives us an idea of how slow or fast that body is moving. For example if a car is running slow, we say that its speed is low. And if a car is running fast, then we say that its speed is high. Therefore, speed of a body is the distance travelled by it per unit time. On the other hand velocity of a body is the distance travelled by it per unit time in a given direction. The speed of a body or here, car gives an idea how fast it is moving. Thus to know the exact position of a moving car we should also know the direction in which the car is moving. So, both speed and velocity is important. We should know the speed of the car as well as the direction of speed. Let us find from this article that why the speed and velocity are not always equal in magnitude.
First we will see how the magnitude of speed and velocity of a moving body is equal.

This will be clearer with the help of an example. Suppose a boy runs a distance of 200 metres in 100 seconds in going from his home to a shop in the East direction in a straight line.
We can calculate the speed of boy i.e. = Distance travelled/Time taken
= 200m/100s = 2m/s
It is important to note here is that the boy runs in a straight line path or in a specified direction, therefore, the displacement will be equal in magnitude to the distance travelled. The displacement will actually be 200m towards East.
Thus, the velocity of boy can be calculated as: Displacement/Time taken
= 200 m towards East/ 100s
= 2m/s towards East
In this case the magnitude or size of speed and velocity of the boy is equal i.e. 2m/s.
Note: The magnitude of speed and velocity of a moving body is equal only if the body moves in a single straight line.

What is the difference between Uniform and Non-Uniform Motion?
But if a body does not move in a single straight line, then the speed and velocity of the body are not equal.
For more clarity we will see an example: Suppose the boy first runs a distance of 200 metres in 100 seconds in going from his home to the shop in East direction, and then runs a distance of 200 metres again in 100 seconds in the reverse direction from the shop to reach back home.

Now, the total distance travelled is 200m+200m = 400m and total time taken is 100s+100s=200s.
Therefore, Speed of boy = Distance travelled/ Time taken
= 400m/200s = 2 m/s
The boy runs 200 m towards East and then 200 m in opposite direction i.e. towards West and reaches at the starting point at home itself. So, the displacement which is distance travelled in a given direction will be 200m – 200m = 0. And the total time 100s +100s = 200s
So, the velocity of the boy = Displacement/ Time taken
= 0m/200s = 0m/s
This means that when a boy first runs at a distance of 200 metres towards East in 100 seconds and then changes the direction and runs the same distance but in reverse direction i.e. towards West in same time, then, his average speed is 2m/s but his average velocity is 0 m/s. So, in this case the magnitude of speed and velocity of the boy is not equal. This happened because boy does not move in a single straight line. He has changed the direction of motion after reaching the shop.
Thus, we can conclude that the average speed of a moving body can never be zero, but the average velocity of a moving body can be zero.

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