Chapter 5, Problem 62P

(III) The position of a particle moving in the xy plane is given by $\stackrel{\to }{r}=2.0\text{cos }(3.0\text{rad/s }t)\hat{i}+2.0\text{sin }\left(3.0\text{rad/s}t\right)\hat{j}$, where r is in meters and i is in seconds. (a) Show that this represents circular motion of radius 2.0 m centered at the origin. (b) Determine the velocity and acceleration vectors as functions of time. (c) Determine the speed and magnitude of the acceleration. (d) Show that a − v²/r. (e) Show that the acceleration vector always points toward the center of the circle.