collision and relative velocity?

Question

There is a head on collision. I need to prove relative veolcity after the collision is equal & opposite to the relative velocity before it. (working only in 1-D) I want to show v1-v2 = - (v1'-v2'). How do I get started?

Answer 1

Conservation of momentum
P = mv before must equal mv after
mass remains the same
velocity is a vecor quantity (magnitude and direction)

Answer 2

Conservation of momentum, in the vector sense.