I know how to find arc length because it's simply a matter of plugging in values into a formula:
s(t) = $\int_a^t |v(u)|\,du$
But given an equation r(t), how do I show whether or not the curves use arc length as a parameter?
e.g) $r(t) = <2 \cos{t}, 2 \sin{t}>$ for $0 \leq t \leq 2\pi$
I did some calculating and figured this much out:
$v(t) = \left< -2\sin{t}, 2\cos{t}\right >$
$|v(t)| = 2$
$s(t) = 2t$
Any examples or tips?