Chapter 12.4, Problem 46E

Motion Along an Involute of a Circle The figure shows a particle moving along a path modeled by

$r(t)=\langle \cos \pi t+\pi t\sin \pi t,\sin \pi t-\pi t\cos \pi t\rangle$.

The figure also shows the vectors v(t) and a(t) for $t=1$ and $t=2$.

(a) Find $a_T$ and $a_N$ at $t=1$ and $t=2$.

(b) Determine whether the speed of the particle is increasing or decreasing at each of the indicated values of t. Give reasons for your answers.