The reason that cars make grinding noises when accelerating is usually a worn out wheel bearing or worn out CV Joint.
If you can jack your car up and spin the wheel by hand you can listen to see if you hear a grinding noise and if you hear a grinding noise when you spin the wheel then it is a wheel bearing.
If it's not the wheel bearing then it likely is the CV Joint and when a CV joint goes bad you have to replace it instead of repairing it.
The CV joint can go bad overtime and they need replaced eventually.
If your car is a manual transmission car then it could an a problem with the clutch.
The grinding noise could also be your brakes but it's usually a worn out wheel bearing or bad CV Joint that causes the grinding noise when accelerating.