Speed of Body under Free Fall from Height

Theorem
Let an object $m$ be released above ground from a point near the Earth's surface and allowed to fall freely.

Let $m$ fall a distance $s$.

Then:
 * $v = \sqrt {2 g s}$

where:
 * $v$ is the speed of $m$ after having fallen a distance $s$
 * $g$ is the Acceleration Due to Gravity at the height through which $m$ falls.

It is supposed that the distance $s$ is small enough that $g$ can be considered constant throughout.