## Conceptual Physics (12th Edition)

If mass stays the same while velocity doubles, the momentum mv turns into m(2v), and increases by a factor of 2. The KE, $\frac{1}{2}mv^{2}$, becomes $\frac{1}{2}m(2v)^{2}$ and increases by a factor of 4. Momentum is proportional to an object's speed, and KE is proportional to the square of the speed.