Thud noise that can be heard and felt?

This is common when the engine torque mount is worn out, I would lift the hood and have a helper start the engine and put the car in gear while the foot is on the brake, then give a little RPM while you watch the engine (off to the side of the car). Then have your helper put the car in reverse so you can watch the engine movement, you should see the engine has excessive movement, here is how to change the mount out in the images below. If you are unsure, please upload a short video of the problem so I can see. Ther mount is under the car near the CV axle on the passages side.