The road might be very bumpy or might have big pebbles on the road.
Maybe that thumping noise is the sound of another car smashing into the rear of your car.
Rotors are worped most likely
Check the heat shield.
If it is a thumping and a front wheel drive car, it is probably one of the axles.
Check the universal joints in the driveshaft.
There are some unknowns here. 1. Did you shut it off and it made a noise, OR 2. Did the car stop running suddenly, making a noise? If you shut the car off, some quiet noises are normal. You may hear the fuel pump from the rear of the car for a couple seconds, and you may hear a solenoid under the hood for a second or two, or the electric radiator fan after the car is shut off. The other question is what kind of noise was it? A loud bang? A whoosh noise, a scrape noise? Did the engine seem to try and keep running? Please add more detail and I'll try to help.
if you try to start the car and it does not start and you hold it in the turn on position do you hear a noise like gears running if so you need a new starter 135 at auto-zone is what i paid for mine but if you don't hear the noise it could be the solenoid
Is it a lifter ticking?
Is an oversized tire rubbing the frame? Is the tire in good repair, or does it have a bubble on the sidewall?
It's called: Your car is running.
It is definitely not a good idea, a thumping noise usually means it has a large bubble, belts are broken or part of the tread is missing. Driving would be unsafe because a blow out of that nature, you could lose control of the car, not able to stop and possibly get into an accident.
The frist thing I would check would be the engine mounts.