Two masses m1 = 2 kg and m2 = 3 kg collide in a perfectly inelastic collision, with m2 initially at rest and m1 moving at 2 m/s. What is the common final velocity?

• A. 0.8 m/s
• B. 1.6 m/s
• C. 2.0 m/s
• D. 0.4 m/s

Answer: (A)

Momentum is conserved in collisions, and when two masses stick together in a perfectly inelastic collision, the final velocity is found from the total initial momentum divided by the combined mass.

The moving mass carries momentum 2 kg × 2 m/s = 4 kg·m/s; the other mass starts at rest, contributing no momentum. After sticking, the total mass is 2 + 3 = 5 kg, so the common final velocity is 4 / 5 = 0.8 m/s in the same direction as the initial motion.

Other values would require final momentum that doesn’t match the initial total momentum (for example, 1.6 m/s would imply 8 kg·m/s, 2.0 m/s would imply 10 kg·m/s, and 0.4 m/s would imply 2 kg·m/s), so they don’t fit momentum conservation.