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.