An object of mass $m$ is initially at rest. When an impulse $I$ acts on the object its final kinetic energy is ${E_{\text{K}}}$. What is the final kinetic energy when an impulse of ${\text{2}}I$ acts on an object of mass ${\text{2}}m$ initially at rest?

A.     $\frac{{{E_{\text{K}}}}}{2}$

B.     ${E_{^{\text{K}}}}$

C.     $2{E_{^{\text{K}}}}$

D.     $4{E_{^{\text{K}}}}$

C

Think proportions.

Twice the impulse on twice the mass would lead to the same final speed. Kinetic energy is proportional to mass (and ${{\text{v}}^{\text{2}}}$, but that doesn’t change) so C must be the correct response.