Question

An empty 2,500 kg train car is headed northbound at a velocity of 5 m/s. Ahead of the first car, an empty 1,500 kg car is headed northbound on the same track at 1 m/s. The faster train bumps into the slower one, and they combine into one train. What is the velocity of the two-car train?

Answer 1

Let the mass of 2500 kg car be $m_1$ and it's velocity be $v_1$ and the mass of 1500 kg car be $m_2$ and it's velocity be $v_2$ .

After the bumping the mass be M and it's velocity be V.

     By law of conservation of momentum we have

                   $m_1v_1+m_2v_2 = MV$

                    2500 * 5 + 1500 * 1=4000 * V

                    V = 14000/4000 = 7/2 = 3.5 m/s

So the velocity of the two-car train = 3.5 m/s