Relation between Momentum and Kinetic Energy

Kinetic energy can also be expressed directly in terms of an object's linear momentum, $\vec p = m\vec v$, which is often the more convenient form when momentum -- rather than velocity -- is the known quantity (as in collision problems).

Starting from $KE = \tfrac12 mv^2 = \tfrac12 m(\vec v\cdot\vec v)$, multiply and divide by the mass $m$:

So:

$KE = \frac{p^2}{2m} \qquad\Longleftrightarrow\qquad p = \sqrt{2m\,(KE)}$ …