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.