Car got rear ended. No body damage. But now upon acceleration or slowing down car will make a popping noise. Popping noise will happen only once per acceleration or slowing down.
Noises can be difficult to diagnose. Follow the above link to get a better idea of what it might take.
In this case I might see if I could replicate the popping noise by bouncing up and down on the vehicle to see if it is a suspension issue. Then maybe have someone rev and torque the engine(in gear) while you look at the engine to see if a motor mount is broken.