My car shakes when I accelerate in reverse, and also when i start up on hills... Could it be a broken motor mount, or what else is there that can cause this?

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1991 Z28 305 1LE, TES headers, 3 Chamber flowmaster, Hi-reving cam... the usual street racer

 

could be a miss under load. make sure your tune up is good. as for broken engine mounts it may be. trans mounts breaking are much more common, you usually hear a thump when you put it in gear from the trans hitting the sheet metal. if it is the trans mount buy a ES poly mount, they're pretty much bullit proof.