Q CAR is a reference to the Q SHIP used in World War 1 & 2.
Essentially they were a decoy Royal Navy ship posing as a merchant
ship used to trick German U -Boats. Unmarked police cars, mainly
highway patrol vehicles use this term as they're covert appearance
is designed to hide the fact they are in service of her Majesty
(like the Q SHIP). The Q originally stood for Quiet, although some
people believe it stands for "Queen's Car".