Problem $3(15$ points$)$ Angle of a rotation object varies with time according to the equation,

$(t)=\frac{}{6}$rad$+(1\mathrm{.}5ra\frac{d}{s^2})t^2$

a$)$ Find the angle of the object at $t=2s.$

b$)$ Find the average angular velocity ${}_{\text{a}\text{v}\text{g}}$ between $t=0$ and $t=2s.$

c$)$ Find the instantaneous angular velocity $$ at $t=2s.$

d$)$ Find the average angular acceleration ${}_{\text{a}\text{v}\text{g}}$ between $t=0$ and $t=2s.$

e$)$ Find the instantaneous angular acceleration $$ at $t=2s.$