Popping noise under harsh acceleration

If I quickly step on the gas from a standstill or slow rolling speed in my 94 Cavalier Automatic, it lurches and there is a popping or grinding noise. What could this be caused by? However, if I am traveling at speeds over 20 and step on it, it accelerates smoothly. I'd be glad to answer any other questions that will help someone figure this out.

I was thinking that it was the A/T fluid level being too low, but when I checked it, it was fine. This car was in an accident, it was side swiped, and that might be adding to the symptoms. The steering pulls to the right. That is all I can think of for right now. Any ideas anyone?

sounds like the suspension maybe... if you put it in reverse and stomp on it does it pop, then pop again when you brake to stop going backwards or put it back in drive to go forwards again??

It only does it when I am going forward. It does not do it in reverse, and it doesn't do it when I am braking. I'm not ruling out anything, so how could this be suspension related?

Just a thought but take a look at oyur engine mounts and see if they have seperated.

I was thinking CV joints or ball joints.