When trying to accelerate from a stop it spit, sputtered and small backfire

I bought the car drove it home ran great. took it on interstate check see if passing gear worked got up to 55 put my foot in it a little passing gear kicked in got up to 65, was satisfied with everything so i got off the interstate stopped at a light. when i went to accelerate it started spitting and sputtering didn't want to get up to speed. so gave her some gas spit and sputtered small backfire strong burning/very strong carbon smell. but it jerked like it wanted to go then once i got over 40 it leveled out smooth. stopped again same thing again. need some advice. whatever happened when i got into it on the highway seems to what started it. need some help please.