In a wash cycle, an automatic washing machine goes into a drying cycle. Starting from rest, it increases its angular velocity at a constant rate up to $8\mathrm{.}0$ s$,$ after which it is rotating at $5\mathrm{.}0$ rev$/$s$.$ At that moment a person opens the lid and a safety switch makes it come to rest in $12$ more seconds. Assume that braking is also with constant angular acceleration.

 a$)$ Calculate the values $$of the angular acceleration in each stage.

b$)$ Draw the graphs of angular position, angular velocity, and angular acceleration versus time, showing the main values.