Question

A 1000 kg car is rolling down the street at 2.5 m/s. How fast would a 2500 kg car have to collide into it in order to bring it to rest (0 m/s)?

Answer 1

initial momentum = 1000*2.5 + 2500 * v = final momentum = 0

v = - 2500/2500 = -1 m/s

Answer 2

Use momentum conservation and assume the cars stick together.
1000*2.5 - (2500)*V = 0
V = 1.0 m/s