A rigid object, hinged at one end and initially at rest, is set into rotational motion. Its angular acceleration is given by the equation

$=$b $+$ ct

where b and c are constants. Here b $=2\mathrm{.}25$ rad$/$s$2,$and c $=3\mathrm{.}40$ rad$/$s$3.$

$($a$)$ Write an expression for the angular speed of the object in terms of the constants b$,$ c$,$ and time t$.$

$=$

$($b$)$ Write an expression for the angular position of the object in terms of the constants b$,$ c$,$ and time t$.$

$=$

$($c$)$ How many revolutions has the object made in the first $9\mathrm{.}35$ s$?$