A speeding person in a car passes a police car, which is parked on the side of the road, at $100$ km$/$h and continues at constant speed. After $2$ s $($seconds$\mathrm{)\; the\; police\; car\; takes\; up\; the\; pursuit\; of\; the\; passenger\; car\; with\; constant\; acceleration.}$

 a$)$ What must the police car's acceleration be to catch up with the passenger car a $1000$m after the passing point? 

 b$)$ What is the final speed of the police car when it catches up with the passenger car?