will having a bad engine motor mount casuse my ford to jerk when accelerating

Easy enough to check for excessive engine movement. Prop the hood up, have a buddy get in, start up the car, apply the brakes, put it in gear (forward and reverse), NEVER TAKE YOUR FOOT OFF THE BRAKE and gently press the gas pedal. This will cause the engine to torque one way or the other. If the engine mount is broken, excessive engine movement will be observed. Never stand in front of the car when doing this just in case the car moves. You don't want to get run over.