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 $A$.

$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

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

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