1989 Grand Prix Accelerates by itself

I have a 1989 Pontiac Grand Prix LE 3.1L with 113000 miles. When the car is not moving the idle is very rough. The RPM will go below 500 and then spike back up to 1500. When the car is moving faster than 5km/h the car will accelerate on its own rapidly. When the car accelerates on its own, the RPM is usually between 1500 and 2000. It is almost as if the gas pedal is being pushed down. When the car is moving and then put into neutral, the RPM will spike to 3000 and stay there until the cars speed is less than 5km/h. Nothing is pushing the pedal down and I have disabled the cruise control by detaching the cable that leads to the throttle.