$1.(8$ pts$)$ While driving his sports car on the highway, Keoni's engine tachometer reads $4000$ rpm $.$ When he sees traffic up ahead, he slows down and brings his vehicle to a stop in $28$ seconds. While idling, his tachometer reads $500$ rpm $.($a$)$ What is his engine's angular acceleration $($in rad$/$s $\backslash (\{\}^\{2\}\backslash ))?($b$)$ How many revolutions has the engine gone through in these $28$ seconds?