Need help with my 370z

drentooth

So I was just driving around last week and stopped to a Red light. After Green light shows up, I hit the gas and as I was accelerating suddenly the car is doing a STOP and GO motion while I was pressing the gas. So I was freaking out and pulled over right away, waited for a couple mins and decided to go again and after that car is fine and didn't do the stop and go motion. This is the first time it happened since I got the car.

Today, I was just cruising around and came to a Red light. After green light, I hit the gas again and as I was accelerating the STOP and GO motion started happening again while I was pressing the gas and SERVICE ENGINE light came on. Idk, what's the problem but I was guessing that it has something to do with the FUEL PUMP or FUEL INJECTORS. Can somebody confirm this for me? I've only owned the car for over a month and bought it preowned. It's AT transmission and I do have warranty for this car