Complete the indicated Be The Cop event during Career mode to unlock the corresponding police car in Quick Play mode.

Dodge Charger SRT-8: Complete the "Clean Up" event in Career mode.
Ford Mustang GT: Complete the "Five-0" event in Career mode.
Lamborghini Gallardo: Complete the "Turn Up The Heat" event in Career mode.
Mitsubishi Lancer Evolution IX: Complete the "Crowd Control" event in Career mode.
Porsche 911 GT2: Complete the "SWAT" event in Career mode.