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?

1 m/s
3 m/s
3.5 m/s
5 m/s

Answer 1

Use conservation of momentum (inelastic collision):

Initial momentum = 2500·5 + 1500·1 = 12,500 + 1,500 = 14,000 kg·m/s.
Total mass after coupling = 2500 + 1500 = 4,000 kg.
Velocity = 14,000 / 4,000 = 3.5 m/s (northbound).

Answer: 3.5 m/s.