  Leibniz suggests that the conservation of relative velocity is rooted in the conservation of the ability of the two colliding bodies to  perform work on one another. The guiding idea here seems to be that  the ability of, say, the balls A and B to act on  one another in virtue of their relative motion, should not be lost at all (at least in idealized cases), so that after a collision they  should continue to have the same ability to act on one another as  they had before they collided, and thus that they should have the  same relative velocity after the collision as they had   before.[26] 