Question

A body goes from A to B with a velocity of $20\,m/s$ and comes back from B to A with a velocity of $30\,m/s$. The average velocity of the body during the whole journey is
A. zero
B. $25\,m/s$
C. $24\,m/s$
D. none of these

Answer 1

Average velocity is given as the ratio of total displacement to total time taken.
${V_{avg}} = \dfrac{{\Delta x}}{{\Delta t}}$
Where $x$ is the displacement ad $t$ is the time taken
Displacement is the straight line distance between the initial and final position of the particle.
Here the initial and final particle is the same.

Complete step by step answer:
Given,
The velocity of the body when it goes from A to B is $20\,m/s$
The velocity of the body when it goes from B to A is $30\,m/s$
We need to find the average velocity.
Average velocity is given as the ratio of total displacement to total time taken.
${V_{avg}} = \dfrac{{\Delta x}}{{\Delta t}}$
Where $x$ is the displacement and $t$ is the time taken.
Velocity is a vector quantity. It has both magnitude and direction.
Displacement is the length of the shortest path taken by an object or it is the straight line distance between the initial and final position of the particle.
In this case, the body goes from A to B and then returns back from B to A. That is, the body returns to the original position. So, the initial position and final position of the body are the same.
The displacement here is zero since displacement is the difference between the initial and final positions

Velocity is the ratio of displacement to time. Since displacement is zero velocity is also zero. Hence the correct answer is option A.

Note:
Don't confuse between average speed and average velocity. The average velocity, in this case, is zero since the total displacement is zero. But that doesn't mean the average speed is zero. Average speed is the ratio of the total distance to total time taken. Distance is the length of the actual path travelled. So, the distance will be twice the length from point A to B. And hence average speed is not zero.