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 y varies with the height h above the ground is correctly shown in

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; just after the collision, it becomes half and in opposite direction. As the ball moves upward, its velocity again decreases and becomes zero at height d/2. This explanation match with graph (A).