Two loaded train cars move toward each other and couple together on impact. The first has a mass of 150,000 kg moving at 0.300 m/s, and the second has a mass of 110,000 kg moving at 0.120 m/s in the opposite direction. What is their common final velocity?

1. Taking the first car's direction as positive, its velocity is +0.300 m/s and the second car's velocity is -0.120 m/s. 2. Because the cars couple together, this is a perfectly inelastic collision, so momentum is conserved while the two masses move off with one common final velocity. 3. Total momentum before the collision is (150000 kg)(0.300 m/s) + (110000 kg)(-0.120 m/s), which is 45000 minus 13200, or 31800 kg m/s. 4. Dividing by the combined mass of 260000 kg gives a final velocity of about 0.122 m/s. 5. The positive sign means the combined cars keep moving in the first car's original direction, not the second car's, and the momentum clearly does not cancel to zero. _Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.3 Conservation of Momentum_