2002 Chevy Cavalier thumping brake.

My 2002 chevy cavalier is making a thump, or popping noise after braking, and begin acceleration. It doesn't do it again until I stop. When I release the brake to accelerate, it pops again. I had the brakes looked at, but I was told that they were in good shape. Otherwise, the car runs and looks like it's new. I've tried to take good care of it, but I don't know what's wrong with it. Can you help ?
Thank you. Sincerely, Roger.