Answer
(a) $40\pi\ rad$
(b) $480\pi\ ft$
(c) $96\pi\ ft/min$
Work Step by Step
Given $r=12\ ft, \omega=8\pi\ rad/min, t=5\ min$, we have:
(a) the angle generated by P in time t is $\theta=\omega t=8\pi\times5=40\pi\ rad$
(b) the distance traveled by P along the circle in time t is $s=r\theta=480\pi\ ft$
(c) the linear speed of P is $v=\omega r=8\pi\times12=96\pi\ ft/min$
