Bad alternator?

Sound like it's on it's way out, also could be a dead cell on the battery and when u got your foot on the gas the alternator is the only thing keeping the battery alive. I think the best idea is to pull the batter and get it check out first at a local auto store ( it's free at autozone i know) If the battery's good then put it back in and take the car and hook up a voltmeter to the alternator and see how much it's putting out. Hope this helps.