Elastic or not, total momentum is always conserved in any collision. So

What is special about an elastic collision is that the total KE before and after the collision is unchanged. So

Dividing (2) by (1):

Notice that *u*_{1} – *u*_{2} represents the relative speed at which *m*_{1} approaches *m*_{2} before the collision, while *v*_{2} – *v*_{1} represents the relative speed at which *m*_{2} separates from *m*_{1} after the collision.

Physically, it means that in any elastic collision, the two bodies approach and separate from each other at the same relative speed.

Mathematically, it means that an elastic collision can be calculated more easily using equations (1) and (3), rather than equation (2).

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