Answer
$K = \frac{p^2}{2m}$
Work Step by Step
We can use the momentum to find an expression for $v$:
$p = mv$
$v = \frac{p}{m}$
We can find an expression for the kinetic energy:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}(m)(\frac{p}{m})^2$
$K = \frac{p^2}{2m}$
