In higher gears when I trap the gas quickly and the car jerks violently I hear a thumping sort of noise from the front right. Also when I drive on grass or bumpy roads I can hear it. The strange thing is when I jog next to the car going about 10 mph with the hood up I can't hear it but my gf driving says she still can... Mount?

 

Sounds like an engine mount. With the engine off, put the car in park (or first if it's a manual trans). Pop the hood, rock the car back repeatedly and watch the engine movement. You may see more motion at one mount. If you do, inspect the rubber in the mount for torn or broken parts.

 

Okay, thanks for explaining it!