What causes car to sputter when giving it gas even though it runs fine when idling?

Sans other problems, my experience dictates that you have a fuel filter that needs changing. Idling? hardly any pressure through the gas lines. Accelerating? pressure builds and, the fuel filter being clogged somewhat, the gas can't get through, and it's choking, so to speak. Try changing the filter. Get a Chilton's mechanic repair book and look at the trouble-shooting chapter, and look for your problem.