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 can be plotted as

For the given condition, initial height h = d and velocity of the ball is zero. When the ball moves downward, its velocity increases and it will be maximum, when the ball hits the ground and just after the collision, it becomes half and in opposite direction. As the ball moves upwards, its velocity again decreases and becomes zero at height d / 2 . This explanation match with graph (a).