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Maybe that thumping noise is the sound of another car smashing into the rear of your car.
CHECK THE EXHAUST.MINE WAS HITTING THE BODY AT BOTTOM OF REAR FENDER
Possibly a broken shock or bad stabilizer bushings
Have that tire checked sometimes the belts inside can break and cause a thumping noise
It could be a suspension part such as a control arm. I just had replace the rear control arms on my 1993 Toyota Celica because the bearings in the control arms were worn out. It made a lot of rattling and thumping; when I replaced the arms the sound stopped.
Bad Tire or wheel bearing, rotate the tires to the front if the noise follows its the tire if remains in rear its the wheel bearing
check the rear drag links for wear the ball joints wear out a lot on them
More than likely the sway bar links - TSB on these
Front Rear End? Does that make sense? Front differential? maybe? Low fluid, wheel bearing, choppy worn tires?
You may have a rear tire out of balance.
The brake rotors are warped. Someone tightened the lugnuts out of sequence. That compressed and torqued the rotors out of spec. Replace the from rotors and pads and the rear ones too, if necessary.
Mine was a busted shock. Look under the car and grab the shock. If you can wiggle it then its bad. If it looks ok I would have it checked by a professional. Good luck