Consider two bodies A and B with masses m1 and m2 moving with velocities u1 and u2 along same line in same direction. Let u1 > u2 .
Suppose the bodies have velocities v1 and v2 after an elastic head-on collision.
Applying principle of conservation of momentum.
Solving the above equations (1) and (2); we get
u1 - u2 = v2 - v1
or velocity of approach before collision = velocity of separation after collision.
Special Cases
(i) B initially at rest i.e. u2 = 0
i.e. the bodies exchange their velocities and momenta.