After being completely stopped (i.e, at a stop light) and then accelarate from that complete stopped position, I hear/feel a grinding noise from underneath the car, towards the back, right side. What could this be?

Thank You

It could be a bad wheel bearing or brake issue. If you have rear disc brakes, clean the caliper pins and lubricate with silicone grease, ensure the pads move freely and are not "metal on metal," and the piston retracts normally and is not frozen. Rear wheel bearings are easy to replace on most vehicles.

A heat shield vibration