Which of the following cannot be the speed – time graph?

Hint: In the question we are given three speed – time graphs. We need to find which of them do not show speed – time relation. To find which one is incorrect, we need to check each of the graphs and see which of them do not obey the conditions of velocity and velocity time relation. Thus we get the solution.

Complete answer:
First let us consider option A.
In this graph we can see that velocity is plotted along the y – direction and time is plotted along x – direction. From this graph we can understand that the speed of the body is always positive and speed has only one value at one time. Therefore this graph exists. Hence it is a correct graph of velocity – time relation.
Now let us consider option B.
In this graph also velocity is plotted along the y – direction and time is plotted along x – direction. As in the option A, speed of the body is always positive and speed has only one value at one time in this graph. And we can also see that the rate of change of velocity is uniform. That is the body in this graph accelerates uniformly. Thus this graph also exists.
Now, by considering the third figure, we can see that velocity is plotted in the y – direction and time is plotted in x – direction. And we can also see that the speed of the body is never negative. But according to the graph, the body has two different velocities at the same time. This is not possible. A body can only have one velocity at one time. Hence this option is wrong.
Therefore we can see that option A and B is correct but C is wrong this proves option D wrong.

Hence the correct answer is option C.

Note:
A graph with speed time relation shows the motion of a body accelerating with a velocity at a time ‘t’.
For a speed – time graph, time will always be plotted along the x – direction and velocity of the body will always be plotted along the y – direction. The slope of such a graph gives us the acceleration of that body and the area under the graph gives us the total distance covered by the body.