A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d/2.$ Neglecting subsequent motion and air resistance, its velocity $v$ varies with height $h$ above the ground as

For the uniformly accelerated/decelcrated motion,

$v^2=u^2\pm 2gh$

So. from this equation. we can say $v-h$ paragraph is parabola.

Initially, velocity is downwards $(-ve)$ after collision, it reverses the direction with smaller magnitude and velocity is upwards $(-ve)$.

So. graph (a) satisfies these conditions.

Also, When $t=0, h=d$ Velocity increases downwards $(\mathrm{U}\to \mathrm{A})$

When $t-1$ velocity reverses its direction $\left(A^{\text{'}}\to B\right)$