loss of power, rough idle, cutsoff when idling

I i recently purchased a 87 535is from s friend that has kept up with fantastic maintance, i had to drive the car almost 3 hours from Richmond VA it did phenomenal the whole drive, but now that i get it home it sits for most of the day but recently actually yesterday i was cruising around 40 then i went to accelerate and it wouldnt accelerate so i gave it more gas and it still wouldnt until i floored it it jumped and knocked into speed. i came up on a red light & at the red light the idle has never been rough at all but at the red light it started shaking so bad it cut off on me so i quickly started it back up and it took forever to get over 25 mph idk what it could be i just want someone to tell me a list of possible problems