mechanical energy. The height doesn't change, so gravitational potential energy is constant throughout. The potential energy stored briefly in the spring is converted back to kinetic energy, so U initial + K initial =  U final + K final which gives 0 + mv 2 + 0  =  mv 1 2 + mv 2 2 which simplifies to v 2 =  v 1 2 + v 2 2 (3). So, combining (2) (conservation of momentum) and (3) (conservation of energy), we have v 1 2 + 2v 1 v 2 + v 2 2 =  v 1 2 + v 2 2 (4). This equation can only be true if v 1 = 0 or if v 2 = 0. So there are two possible solutions. One is v 1 = 0 and v 2 = v, which is what we see in the clip above : the left car comes to a complete stop and the right car leaves the collision with v. The other solution is v 1 = v and v 2 = 0, which is what happens if they don't collide at all. (Strictly, the second solution is possible only in two or three dimensions, not one.) The example below shows a more general case: in the frame of the camera, the initial velocities of the two cars are in opposite directions and have different magnitudes. Initially, the car on the left is travelling faster, so the centre of mass is moving to the right, which