For the given displacement-time graph,what wi | vedclass

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(A) The velocity $v$ is given by the slope of the displacement-time $(s-t)$ graph,i.e.,$v = \frac{ds}{dt}$.In the given $s-t$ graph,the curve is a par

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(A) The velocity $v$ is given by the slope of the displacement-time $(s-t)$ graph,i.e.,$v = \frac{ds}{dt}$.In the given $s-t$ graph,the curve is a parabola opening downwards,which can be represented by the equation $s = at - bt^2$,where $a$ and $b$ are positive constants.Differentiating this with respect to time $t$,we get the velocity $v = \frac{ds}{dt} = a - 2bt$.This equation $v = a - 2bt$ represents a straight line with a negative slope $(-2b)$ and a positive intercept $(a)$ on the velocity axis.Thus,the velocity-time graph is a straight line with a negative slope,which matches the graph shown in option $A$.

Graph	Characteristics
$(A)$	$(i)$ has $v > 0$ and $a < 0$ throughout
$(B)$	$(ii)$ has $x > 0$ throughout and has a point with $v = 0$ and a point with $a = 0$
$(C)$	$(iii)$ has a point with zero displacement for $t > 0$
$(D)$	$(iv)$ has $v < 0$ and $a > 0$

For the given displacement-time graph,what will the corresponding velocity-time graph look like?

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