Your gas tank sender might be bad causing a reading that is not correct so instead of being on empty its on still about 1/4 tank. The acceleration would suggest that as you speed up the gas is transferring away from the inlet for the engine causing fuel starvation problems. Keep the car gassed up or look into checking the stuff that reads the tank level and sends it to your dash, if that doesn't do it then there is something else going wrong between the tank and the engine.