Question

A railroad car with a mass of 30,000 kg is moving at 2.0 m/s when it runs into an at-rest freight car with an equal mass. The cars lock together. What is their final velocity?

Answer 1

The total momentum of the system is preserved through the collision.

Note that momentum is
P = m*v
where m = mass
v = velocity.

Initial momentum:
P1 = (30000 kg)*(2 m/s) = 60000 (kg-m)/s for the moving car
P2 = 0 for the starionary car.

Final momentum:
P3 = (30000 + 30000)*v = 60000v (kg-m)/s

Because momentum is preserved,
P3 = P1 + P2
60000v = 60000
v = 1 m/s
The final velocity is 1 m/s.

Answer: 1.0 m/s