$($II$)$ The angle through which a rotating wheel has turned in time t is given by $=9\mathrm{.}5$ t $-13\mathrm{.}0$t$^2+1\mathrm{.}6$t$^4,$ where is in radians and t in seconds. Determine an expression $($a$)$ for the instantaneous angular velocity w and $($b$)$ for the instantaneous angular acceleration a$.($c$)$ Evaluate w and a at t $=3\mathrm{.}0$ s$.($d$)$ What is the average angular velocity, and $($e$)$ the average angular acceleration between $1=2\mathrm{.}0$s and t $=3\mathrm{.}0$ s$?$