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Question 26

The best representing   velocity -time ($$v-t$$) graph corresponding to displacement -time ($$s-t$$ ) graph shown is

image

To find the velocity-time graph, we need to remember that velocity is given by the slope of the displacement-time graph.

$$$v=\frac{ds}{dt}$$$

In the first horizontal segment, the displacement does not change with time. So, its slope is zero and hence, $$v=0$$.

In the rising segment, the displacement increases uniformly with time. Therefore, the slope is positive and constant, say $$v=a$$.

In the steep falling segment, the displacement decreases rapidly. So, the slope is negative and has a larger magnitude, say $$v=-b$$.

In the next horizontal segment, the displacement is constant again, so $$v=0$$.

In the final falling segment, the displacement decreases with a smaller negative slope. Hence, $$v=-c$$.

Therefore, the velocity changes as $$$0\rightarrow a\rightarrow-b\rightarrow0\rightarrow-c$$$.Hence, the correct answer is $$B$$.

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