When two objects collide, their initial contact sets up a compression wave that passes through each of them. For a short duration after initial contact, parts of the objects continue to move as if nothing had happened. Only after the compression wave passes through and reflects back might the two objects separate again. Different forces are at work within the objects, causing them to flex and compress/expand. A complete study of what is happening would need a very detailed knowledge of the materials in the objects and the forces set up within them by the impact. And we have not even taken friction or air resistance into account.
Fortunately, if we simply wish to compare the motion of the objects before the impact with their motion after, then much of this detail can be omitted. It is useful to refer to all of the objects involved in a collision as a ‘system’.
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