Now consider a situation which we could call an inverse collision in which
two objects are initially at rest. For simplicity and because it does have some
practical relevance we
choose the one-dimensional case. An internal event causes the objects to
separate and move with in general different final velocities 
and
. Clearly no external forces act on this system so momentum is conserved:
and must remain zero at all times
This equation clearly is not enough to determine the velocities, we must know
something about how much internal energy is converted to kinetic
energy. We denote this energy 
and requirement that as
always energy is conserved gives us
We now have two equations with two unknowns from which we can determine
the final velocities to be
We cannot determine the directions but we now that they will be opposite.
Note the beautiful symmetry in these expressions upon interchanging the indices.
We certainly should require the physical situation is not changed
by re-labeling the particles. I leave you to derive these expression your self.
They become especially simple in the case where the objects have equal masses:
We will perform two experiments to illustrate the inverse collision