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?

First thing to do it inspect and repair any problems with the brakes. I would bet once you replace your brake pads the noise will disappear.