Chapter 12.6, Problem 10ES

Suppose that a particle vibrates in such a way that its position function is $\text{r(}t)=16\sin \pi t\text{i}+4\cos 2\pi t\text{j,}$ where distance is in millimetres and $t$ is in seconds.

(a) Find the velocity and acceleration at time $t=1\text{s}.$

(b) Show that the particle moves along a parabolic curve.

(c) Show that the particle moves back and forth along the curve.