In English a phrase can be converted into an instruction by applying positive intonation (raising the tone of the voice towards the end of the phrase). For example "in the car" as a phrase is relatively meaningless as it has no subject but by applying positive intonation "in the car!" it becomes an instruction equivient to "get in the car" with the subject being implied as the person you are talking to.

Can the same be done in Turkish???
For example can I say to someone or something (like my dog) "arabada!" as an instruction to get into the car or does it need an explicit subject such as:

Arabada köpeğim!

I think I understood what you have asked. And I can see that you think that situation in English just like I sometimes think in Turkish. Actually you are right. But the only difference is that, according to your example, you translate the preposition "in" literary to Turkish. Thus the turkish equivalent of the phrase you gave as example becomes "arabada!". But "arabada" shows a state of position. On the other hand, as far as I understand, it must show a state of direction like "into" or "toward" from angle of the meaning. Right? If so, you could say in turkish:

"Arabaya!"(Toward to the car!!!). It means "Arabaya bin!"(get in the car!) or "Arabanın içine gir".

And there is no need any subject or object in imperative structures as you will always be the first person and order the second person.