Let m 1 , m 2 be the mass of object 1 and object 2 respectively. Let u 1 , u 2 be the initial velocity of object 1 and object 2 respectively. Let v 1 , v 2 be the final velocity of object 1 and object 2 respectively. { 1 2 m 1 u 1 2 + 1 2 m 2 u 2 2 = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 m 1 u 1 + m 2 u 2 = m 1 v 1 + m 2 v 2 From the first equation, m 1 ( u 1 2 − − v 1 2 ) = m 2 ( v 2 2 − − u 2 2 ) m 1 ( u 1 + v 1 ) ( u 1 − − v 1 ) = m 2 ( v 2 + u 2 ) ( v 2 − − u 2 ) From the second equation, m 1 ( u 1 − − v 1 ) = m 2 ( v 2 − − u 2 ) After division, u 1 + v 1 = v 2 + u 2 u 1 − − u 2 = − − ( v 1 − − v 2 ) | v 2 − − v 1 | | u 1 − − u 2 | = 1 The equation above is the restitution equation, and the coefficient of restitution is 1, which is a perfectly elastic collision.