Can this be "He stops right there"? Duo marked it wrong. In English, it is more common to say "He stopped the car" than "He braked the car".
Indeed! It has maaany meanings, specially when it follows other words... (like "to get" in English) =)
It is, very weird.....I only could understand it's weirdness when I met "ja" and "doch" in German. (Although I cannot say that mesmo is equivalent to "ja" - because I just don't understand "ja" yet - I'd risk saying there is some resemblance....or maybe doch?)
In this case, and lots of other cases "mesmo" works as an "assurance" word. It adds an idea that he doesn't brake or doesn't need to brake anywhere else, but "aí mesmo" is ok.
So this "mesmo" is like assuring that it's nowhere/nothing else, as if there is or would be a question about the place.
This case can also be seen in contructions like "ele mesmo vai...." (he goes himself - not anyone else...)
When I see this "mesmo", this is what comes in my head:
"Aí mesmo" = don't go imagining alternative solutions or places to brake, just brake right there. Don't bother thinking about other things, this is enough...
Its a weird sentence in english. You have to go out of your way to think of a context where it makes sense.