Sounds like it may be a worn "front" motor mount. This one is located behind the vibration dampener at the front of the engine. Remove the passenger side front wheel and lift up on the wheel well access cover after removing the two plastic nuts. Jack the engine up and check if the motor mount rubber is split. The metal part of the mount may be rubbing on the frame. It is relatively easy to replace and a good quality one runs around $75. They usually go bad any time after 75K miles.