Why is my battery light going on when I accelerate?

I recently bought a Honda accord 1997. The car turned on it ran a test drive that and everything was great now when I turned it off I have bought the car ready the guy left that I bought it from. I try to turn the car back on. It didn't even turn over not even clicking so I figured I needed a jump and then I got a jump and then it died again. So I figured I needed a new battery so I bought a new battery put it in and the car runs fine but now the problem is, when I accelerate the battery light turns on why would my battery light turn on?

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