The general name for cars with 'Police' markings would be a 'police car.' However there are different types of police cars. The car in the picture seems to be car capable of high speeds and so is probably in the category of 'police pursuit vehicle.' Theis term is sometimes abbreviated to 'PPV'.
"What happened to John?"
"He was just taken away in a police car."
"Oh dear!"
警察の載っている車のことを一般的にはpolice carと言います。色んな種類のpolice carがあります。スピードのでるような車なら、恐らくpolice pursuit vehicleでしょう、略されてPPVと言われたりします。
"What happened to John?" ジョンはどうしたんだ?
"He was just taken away in a police car." パトカーで連行されてったよ。
"Oh dear!" なんてこったい。
A POLICE PATROL VEHICLE. or simply put...A police car!
We noticed a police car was following us, so we kept our speed down!
We all need to be respectful of law enforcement officers...and when we see this vehicle we should mind our P's and Q's (idiom)
This vehicle is known as a police car or a patrol car. They can be seen on the streets making sure people aren't going too fast or running red lights.
Informally a policeman is also known as a cop, and the vehicle is thus known as a cop car. The term is perfectly fine to use.