Question

The velocity of a particle moving in a straight line is given by the graph shown here. Draw the acceleration position graph.

Answer 1

$v-v_0=\frac{-v_0}{x_0}x\Rightarrow v=v_0-\frac{v_0}{x_0}x$
$\Rightarrow \frac{dv}{dx}=\frac{-v_0}{x_0}$
$\Rightarrow \frac{vdv}{dx}$ $=(v_0-\frac{v_0}{x_0}.x)-\frac{v_0}{x_0}$ $=\frac{-v_0^2}{x_0}+\frac{v_0^2}{x_0^2}x$