A wheel $2\mathrm{.}40$ m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of $3\mathrm{.}90$ rad$/$s$2.$ The wheel starts at rest at t $=0,$ and the radius vector of a certain point P on the rim makes an angle of $57\mathrm{.}3$ with the horizontal at this time. At t $=2\mathrm{.}00$ s$,$ find the following.

$($a$)$ the angular speed of the wheel

rad$/$s

$($b$)$ the tangential speed of the point P

m$/$s

$($c$)$ the total acceleration of the point P

magnitude m$/$s$2$direction $$ with respect to the radius to point P

$($d$)$ the angular position of the point P

rad