The velocity (v) versus displacement (x) plot | vedclass

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(D) The acceleration $a$ is given by $a = v \frac{dv}{dx}$.From the given graph,the velocity $v$ is a linear function of displacement $x$.For the inte

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(D) The acceleration $a$ is given by $a = v \frac{dv}{dx}$.From the given graph,the velocity $v$ is a linear function of displacement $x$.For the interval $0 \le x \le 100$,the slope is positive. Let $v = kx$ (where $k > 0$). Then,$a = v \frac{dv}{dx} = (kx)(k) = k^2 x$. This shows that $a$ increases linearly with $x$ in this interval.For the interval $100 \le x \le 200$,the slope is negative. Let $v = -k(x - 200) = -kx + 200k$. Then,$a = v \frac{dv}{dx} = (-kx + 200k)(-k) = k^2 x - 200k^2$. This shows that $a$ increases linearly with $x$ in this interval,but with a negative intercept.Comparing this with the given options,the graph that shows a positive linear increase in acceleration for the first part and a positive linear increase with a negative value for the second part is option $D$.

The velocity $(v)$ versus displacement $(x)$ plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration $(a)$ as a function of displacement $(x)$ is

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