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+2 votes
in Physics by (2.8k points)

Among the four graphs shown in the figure, 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?

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+3 votes
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Ans. (b) In graph (b) for one value of displacement there are two different points of time.
Hence, for one time, the average velocity is positive and for other time is equivalent negative.
As there are opposite velocities in the interval 0 to T hence average velocity can vanish in (b). This can be seen in the figure given below.
Here, OA = BT (same displacement) for two different points of time.

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B is the correct option as you can see that DX/dt of any graph give the velocity, and velocity banner say that means DY by DX equal to zero, this conclude that there must be a Maxima or minima, another function the graph either strictly increasing or strictly decreasing, in graph B there is only a maximum or minimum so velocity can be zero

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