In a head-on elastic collision between two identical masses, which description matches the final speeds?

• A. The speeds are exchanged; the moving mass stops and the other moves with the original speed.
• B. The moving mass continues with the same speed.
• C. The initially stationary mass moves at speed v and the moving mass stops.
• D. Both masses move away with equal speeds.

Answer: (C)

In a head-on elastic collision between equal masses, the velocities swap in one dimension. Here one mass starts with speed v and the other is at rest, so after the collision the initially moving mass ends up with zero velocity and the initially stationary mass takes on the speed v in the same direction. This comes from conserving momentum (m v + m·0 = m v1' + m v2') and kinetic energy (1/2 m v^2 = 1/2 m v1'^2 + 1/2 m v2'^2), which together yield v1' = 0 and v2' = v (up to labeling). So the final state is that the stationary mass moves at speed v while the moving mass stops.