Problem

The key is recognizing that momentum and kinetic energy scale differently with velocity. Since momentum $p = mv$ increases by 50%, the velocity increases by 50% too. But kinetic energy $KE = \frac{1}{2}mv^2$ depends on $v^2$, so a 50% velocity boost creates a much larger energy boost—you need to square the velocity factor to find the new kinetic energy.

The key is recognizing that momentum and kinetic energy scale differently with velocity. Since momentum $p = mv$ increases by 50%, the velocity increases by 50% too. But kinetic energy $KE = \frac{1}{2}mv^2$ depends on $v^2$, so a 50% velocity boost creates a much larger energy boost—you need to square the velocity factor to find the new kinetic energy.