An interesting, special case of an elastic collision is a collision in which one of the objects is initially at rest (v2i = 0).
Click on an example below to watch an animation.
An interesting situation is when the two masses are equal. For m1 = m2, we find that
v2f = v1i
This is illustrated with the "colliding balls" apparatus shown here, also known as "Newton's Pendulum".
(C) 2002, Doug Davis; all rights reserved