Path Length

Theorem: Path Length

The length of the path which a Point Mass $P$ follows from time $t_1$ to time $t_2$ is the line integral of its speed between the two moments:

$${\int }_{t_1}^{t_2}||\mathbf{v}(t)||\mathrm{dt}$$

PROOF

This is just the formula for finding the length of a curve.