Question

The kinetic energy of an object is increased by a factor of 8, by what factor is the magnitude of its momentum changed?

Answer 1

kinetic energy: $E_k=\frac{1}{2}mv^2$

momentum: $p=mv$

where $v$ - velocity, m - mass

$\implies p=\sqrt{2mE_k}$

if $E_k$ is increased by a factor of 8 then $p$ is increased by a factor of $\sqrt8 \approx2.8$

Answer: $\sqrt8 \approx2.8$