Two equal masses m = 1 kg each on a frictionless track collide elastically head-on with equal and opposite speeds of 3 m/s. What are their speeds after the collision?

• A. They exchange velocities; each moves at 3 m/s in opposite direction
• B. One stops and the other goes 3 m/s
• C. Both move forward at 3 m/s
• D. They pass through without changing speeds

Answer: (A)

In a one-dimensional elastic collision on a frictionless track, momentum and kinetic energy are conserved. With equal masses and equal but opposite initial speeds, the most straightforward way to satisfy both conservation laws is for the bodies to swap velocities.

Here, one mass starts at +3 m/s and the other at -3 m/s. After the collision, momentum conservation gives v1' + v2' = 0, so the final velocities are opposite: v2' = -v1'. Kinetic energy conservation requires v1'^2 + v2'^2 = 18 (since each mass has initial kinetic energy 1/2 m v^2 = 9, totaling 18 for m = 1). Substituting v2' = -v1' gives 2 v1'^2 = 18, so v1' = ±3 m/s and v2' = ∓3 m/s. The physically consistent outcome is that they exchange velocities: one ends up with -3 m/s and the other with +3 m/s.

Thus each ends with a speed of 3 m/s, but in opposite directions—the velocities have swapped.