Question

A body travels from A to B at $40 ms^{-1}$ and from B to A at$60 ms^{-1}$`. calculate the average speed and the average velocity.

Answer 1

Hint: In the question, we have given two different speeds to cover the same distance. First, we will find the average speed by the formula. As the body reaches its initial position again, so displacement of the body is equal to zero. Average velocity is the total displacement divided by time taken. So, we get an average velocity of zero.

Complete answer:
Average speed is the ratio of total distance travelled to the total time taken.
Average speed = $\dfrac{2 V_{1} V_{2}}{ V_{1} + V_{2} }$
$ V_{1} = 40 ms^{-1}$
$ V_{2} = 60 ms^{-1}$
Put the values of both the velocities.
Average speed =$\dfrac{2 \times 40 \times 60}{ 40 + 60 }$
Average speed $= 48 ms^{-1}$
Average velocity is the ratio of total displacement to the total time taken.
A body travels from A to B and then from B to A.
Initial and final position is the same.
So, displacement is zero.
This gives average velocity is equal to zero.
Hence, average speed is $ 48 ms^{-1}$ and average velocity is zero.

Note:
There is a variation between average speed and average velocity because the average speed is measured as the total distance covered by a body divided by the total time taken, while average velocity is defined by the displacement divided by the total time taken. Both quantities have the same unit.