it sounds like the car needs a tune up ... Spark plugs/ wires/ oxygen sensor .... That should take care of the problem.
What Does It Mean When A Car Hesitates When Accelerating?
Sorry, that was vague.... The problem happens when the car is cold and has not been shifted out of first gear yet. The first time I accelerate through first and second gear, the car accelerates very slowly until it gets to 3000-4000 RPM, and then it jumps forward. I'm positive I am not doing this with my foot on the accelerator pedal, it's only when the car hasn't been driven for a few hours and only the first two or three times I shift. The car is nearly brand new with just over 8000 miles on it.