At the title screen, press R2, R2, R2, L1, Triangle, L2, L2, L2, R1, Square.
Face Off Mode:
Beat championship mode once to open "Face Off" mode against the Roadster.
Roadster:
Beat the Roadster in Faceoff mode to unlock it.
Get Tow Truck:
Beat the Tow Truck in Faceoff #2 to unlock it.
Saloon GT:
Beat the Saloon GT in Faceoff #3 to unlock it.
Bus:
Beat the Bus in Faceoff #4 to unlock it.