When two objects collide in an elastic collision, aren't there an infinite number of possible velocities that the objects can gain? Let's consider two objects each of mass 1kg. One of them is moving at 1 ms-1 and the other is stationary. After the collision, the first object (the one which was moving) could come to rest and the other object could start moving at 1 ms-1. That's one scenario in which the 1st object transfers all it's kinetic energy to the other object. Couldn't the first object keep some of it's energy and only transfer a fraction of it's total KE to the other object? (In which case both objects would be moving after the collision). If that happens, then couldn't there be a several pairs of values for the velocity of Object 1 and object 2 which would comply with the conservation of momentum and the conservation of kinetic energy? How can we determine which one of these combinations of velocities will occur ?