A billiard ball traveling at 3.8 m/s has an elastic head-on collision with a billiard ball of equal mass that is initially at rest. The first ball is at rest after the collision. What is the speed of the second ball after the collision?

Answer 1

The only way to conserve both kinetic energy and momentum for the second ball to acquire the velocity of the first ball, if the first ball stops.

That is what happens in a head-on elastic collision.