A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration $0\mathrm{.}142$ rad$/$s$?.$ After making $2870$ revolutions, its angular speed is $148$ rad$/$s$.($a$)$ What is the initial angular velocity of the turbine? $($b$)$ How much time elapses while the turbine is speeding up$?$