Two bodies of identical masses with `2^(nd)` body at rest collides with `1^(st)` body, prove that the velocities of the bodies are reversed.

Explanation

When bodies have the same mass i.e., `m_(1)=m_(2)` and second body (usually called target) is at rest `(u_(2)=0)`,
By substituting `m_(1)=m_(2) and u_(2)=0` in equations
`v_(1)=((m_(1)-m_(2))/(m_(1)+m_(2)))u_(1)+((2m_(2))/(m_(1)+m_(2)))u_(2)" "...(1)`
and equations
`v_(2)=((2m_(1))/(m_(1)+m_(2)))u_(1)+((m_(2)-m_(1))/(m_(1)+m_(2)))u_(2)," we get ...(2)"`,
from equations (1)
`implies v_(1)=0`
from equations (2)
`implies v_(2)=u_(1)`