It actually shocked me when I first taught ESL that there was actually a pretty good English rule for the order in which we use adjectives before a noun.
Intuitively a native English speaker arranges the adjectives properly. However, if you ask them why they did it a particular way, they will respond that it just sounds better. The answer that it "does not sound right" does not help English learners, does it?
The rule for English adjectives is that they must follow a specific order.
number/opinion/size/shape/age/colour/origin/material
So we say,"nice round yellow wooden table" not "yellow wooden nice round table"
We say "ancient English wooden clock" not " English wooden ancient clock"
It is not a perfect rule and you sometimes have to make a judgement call on your part as to what category your adjectives fit in. That is the case with your adjectives of "unmarked" and "police".
I would use the process of elimination in my decision.
Take "police" for example. Is this adjective a number, opinion, size, shape, age, colour or material? No... it would be an "origin" adjective.
Take "unmarked". This is more difficult to decide except that it definitely is not a "material" or "origin" so it would be placed before "police"
So, "unmarked police car" would be the right choice.
Sometimes you might want to purposely ignore this rule. For example you might say
"I want the old red table".
This is the normal proper way to write or say this sentence. However, say you were annoyed that your request was ignored.
In frustration you might say "I want the red old table! This old table is pink." By saying the adjectives in the wrong order would emphasize what is important to you.
Of course, from a speaking English point of view you could also just emphasize the colour "red" to show your frustration saying " I want the old RED table! This old table is pink."
In my opinion speaking English not taught as much as it should be.
