Question

Among the four graphs, there is only one graph for which average velocity over the time interval $ (0, T) $ can vanish for a suitably chosen $ T $ . Which one is it ?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Average velocity: It is defined as the ratio of displacement to time taken by the body. Average Velocity $=\frac{\text { Displacement }}{\text { Time Taken }}$ According to this problem, we need to identify the graph which is having the same displacement for two timings. When there are two timings for same displacement, the corresponding velocities should be in opposite directions. As shown in graph (b), the first slope is decreasing that means particle is going in one direction and its velocity decreases, becomes zero at highest point of the curve and then increasing in backward direction. Hence the particle return to its initial position. So, for one value of displacement there are two different points of time and we know that slope of $x, x$-t graph gives us the average velocity. Hence, for one time, slope is positive then average velocity is A also positive and for other time slope is negative then average velocity is also negative. As there are opposite velocities in the interval o to T, hence average velocity can only vanish in option (B) This can be seen in the figure given alongside. As shown in the graph, OA = BT (same displacement) for two different points of time