At its lowest setting a centrifuge rotates with an angular speed of $250$ rad$/$s$.$ When it is switched to the next higher setting it takes t $=5\mathrm{.}5$ s to uniformly accelerate to its final angular speed $=750$ rad$/$s$.$ Part $($a$)$Calculate the angular acceleration of the centrifuge a$,$ in rad$/$s$?$ over the time interval t$.$Part $($b$)$Calculate the total angular displacement $($in radians$)$ of the centrifuge, delta theta, as it accelerates from the initial to the final speed.