Engine Grinding sound on acceleration.

Manual or automatic trans? If manual, how many miles on the clutch? Mine made a similar sound at idle and low gears and it ended up being the throwout bearing being shot.

Sounds possibly like a bad motor mount or transmission mount? Look underhood for witness marks where something on the body is contacting something on the engine or under the car for exhaust that is rubbing a cross member or something. Also check to see if it can be reproduced by holding the brake pedal and throttling slightly such as powerbraking.