Question

When does the average velocity become zero?

Answer 1

Hint: The average velocity can be defined as the total displacement divided by the time taken to make the displacement. We can recall that displacement is a vector quantity and hence depends on the direction.

Formula used:
In this solution we will be using the following formulae;
 $ \bar v = \dfrac{d}{t} $ where $ \bar v $ is the average velocity of an object, $ d $ is the total displacement, and $ t $ is the time taken to make such displacement.

Complete Step-by-Step solution
We are to define the state at which the average velocity of an object will be equal to zero. To do this, we have to define the average velocity itself.
The average velocity is the total displacement divided by the time used to change the displacement. Mathematically given as
 $ \bar v = \dfrac{d}{t} $ where $ \bar v $ is the average velocity of an object, $ d $ is the total displacement, and $ t $ is the time taken to make such displacement.
Hence, generally, when the total displacement is zero the average velocity is zero.
For a better understanding, recall that the displacement of a body is a vector and hence is dependent on the direction. It is specifically defined as the rate of change of position of the object in a specified direction. This means that when a body changes position in a particular direction at first, and changes the position in the opposite direction by the same amount, the displacement is zero.

Note
Also, for a uniformly accelerating body, the average velocity is zero if the final velocity is equal to the negative of the initial velocity. For example, a body thrown vertically upward under gravity only, will accelerate uniformly downward (acceleration due to gravity), and have the same velocity at the end as it had at the beginning. The average velocity in such a case is zero.