Two stones are thrown up simultaneously from the edge of a cliff with initial speed v and 2v. The relative position of the second stone with respect to first varies with time till both the stones strike the ground as

Initially when both are in air, the relative acceleration between them is zero. Therefore, relative position versus-time graph is a straight line. Once the first ball reaches the ground, its acceleration becomes zero. Therefore, the relative acceleration is now g and the graph is parabolic.