Express momentum in terms of mass and kinetic energy.

(N/A) The kinetic energy $K$ of an object of mass $m$ moving with velocity $v$ is given by $K = \frac{1}{2}mv^2$.
Multiply and divide the expression by $m$:
$K = \frac{1}{2} \frac{m^2v^2}{m} = \frac{(mv)^2}{2m}$.
Since momentum $p = mv$,we can substitute $p$ into the equation:
$K = \frac{p^2}{2m}$.
Rearranging for $p$:
$p^2 = 2mK$.
Therefore,the momentum is $p = \sqrt{2mK}$.