Car makes noise when accelerating at very low speeds?

I have a Honda Accord and I've noticed that when my car is not moving and I press lightly on my gas pedal it starts to making a grinding noise until I reach a certain speed around 10-15 mph. But from 0-10 mph it makes a grinding noise as I press lightly on the accelerator. I thought that maybe it's my brakes because my brakes make a slight grinding noise even when I'm not pressing down on them. But this sound with the gas pedal is new. What could this possibly be?

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