A railway car of mass m1 travelling at a velocity of v1 collides with a second car of mass m2 travelling at v2 and the two join together. What is their final velocity?

Momentum is conserved in any collision, and for a single body is given by p = mv. The momentum before is m1v1+m2v2, and the momentum after is (m1 + m2)u where u is the final velocity, so the final velocity is (m1v + m2*v2)/(m1 + m2).