1995 Pontiac Grand Am 95 Grand Am Shuts off after coming to

My car runs well except when I reach 50mph at which point the car begins to vibrate. Then, occasionally, when I come to a stop (for instance at a toll booth) the car begins to shake and then eventually turns off when I come to a stop. I find that this happens most frequently after reaching higher speeds (50mph+). If I try to turn the car on again it starts up, but when I put the car in drive and hit the gas it instantly turns off again. If I wait for a little while or have my friend push the car and shift to drive the car will operate normally again, as though the speed from my friend's pushing helped the car in some way.

I apologize if this is confusing or difficult to follow. Please ask questions if something needs further explanation. Thanks.