Suppose that an object has a certain speed, kinetic energy, and momentum. If the object's speed increases until it has 4 times the kinetic energy that it had before, then its momentum is
A) 2 times greater than before.
B) unchanged.
C) 16 times greater than before.
D) 4 times greater than before.

Question

Quizplus · Accepted Answer

The kinetic energy (KE) of an object is given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity. If the kinetic energy becomes 4 times greater, it implies that $v^2$ has become 4 times greater (since mass $m$ is constant), meaning $v$ has become 2 times greater. Momentum ($p$) is given by $p = mv$. Therefore, if $v$ doubles, $p$ also doubles.

Suppose That an Object Has a Certain Speed, Kinetic Energy