Why would a car sputter while driving but quit as soon as a speed up or slow down?

Why would a car sputter while driving but quit as soon as a speed up or slow down?
There could be a number of reasons for this you car could be running to rich. If its coughing black smoke out the back and is a petrol it is running to rich (a diesel coughing black smoke is also not burning its fuel efficently). Think of it this way black smoke weather its from a petrol or diesel is wasted fuel, fuel you have payed for and not got any gain out of and this can cause this, it can also be missing, there can also be water getting into the ignition of the car which will also cause this, blown head gasget if there is coulds and coulds of white steam coming from the exaust and the engine won't run propably that could also be the reason. My guess is that the engine is runing to rich tho but sounds like you need to take it somewhere.