Prove that bodies of identical masses exchange their velocities after head-on elastic collision.

Explanation

When bodies have the same mass i.e.,
`m_(1)=m_(2)`
`v_(1)=((m_(1)-m_(2))/(m_(1)+m_(2)))u_(1)+((2m_(2))/(m_(1)+m_(2)))u_(2)`
`v_(1)=(0)u_(1)+((2m_(2))/(2m_(2)))u_(2)`
`v_(1)=u_(2)`
`v_(2)=((2m_(1))/(m_(1)+m_(2)))u_(1)+((m_(2)-m_(1))/(m_(1)+m_(2)))u_(2)`
`v_(2)=((2m_(1))/(2m_(1)))u_(1)+(0)u_(2)`
`v_(2)=u_(1)`