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 the height h above the ground as 

While taking downward motion of ball, its velocity at height h, using the relation,  $v^2=u^2+2aS,$ is $v=\sqrt{2g(d-h)}$ 
It means of h=d, the velocity of ball zero, while taking upward motion of ball, the velocity of ball at h=0, should be finite say u but less than what it has during fall, since the ball has to go upto a height d/2. Using the relation,  $v^2=u^2+2$ as the velocity of the ball at height h is,  $v=\sqrt{u^2-2gh}$. With the above considerations, we note that the variation of v and h will be as given by Figure.