Question

Which of the following velocity (V) – time (t) curves do not represent motion of a body?
A.

B.

C.

D.

Answer 1

Hint : Velocity of a body is defined as the rate of change of the position of the body with respect to time. To find the graph that does not represent the motion of a body use the fact that a body can have only one velocity at a given time.

Complete step by step solution :
When a body is motion, we know its position with respect to a reference point. What we do is we locate its position as the body continuous moves. The quantity that changes with the motion of the body is time. We say that the body starts its motion at time t = 0. Then time passes, we locate the position of the body. It helps to keep a track of the position of the body that has already occurred if we know the time at which it occurs.
To understand the motion of the body even better, we define its velocity. Velocity is the rate of change of the position of the body with respect to time. In other words, the change in position of the moving body in one unit of time.
Velocity of a body can be positive as well as negative because change in position can be positive or negative.
Velocity can be in positive direction or in negative direction. However, time is always in the forward direction. The meaning of this is that time does not depend on any factor. Time always passes away and we cannot bring it back. In other words, we can only travel in the future and can never return to the past. Time is always increasing.
Therefore, a body can never go back in time. Hence, the body cannot velocity at a time that has already passed away. In other words, a body cannot have two different velocities at same time.
However, in the graph in option B, we can see that the body has two different velocities at a given time. Therefore, this graph does not represent the motion of a moving body.
Hence, the correct option is B.

Note : If we see the graphs in other given options, at a given time the body has a unique velocity. Therefore, these motions of the body exist. Hence, they represent the motion of a body.