One problem related to car accelerates on its own has been reported for the 2001 Volvo V70. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2001 Volvo V70 based on all problems reported for the 2001 V70.
My wife was driving our Volvo xc (2001) back from the grocery store. In exiting the store parking lot she had make a left turn onto rt. 24w in mendham, NJ from a stop sign. As she got on to the single lane highway the car stalled leaving her without power in the middle of a single lane highway with our 2 year old son in the back seat. Incoming traffic suddenly had to come to a stop in order not to hit her car. She was able to move the car to the side of the road and restart it and make the 5 minute trip back home. The car was not able to make the slight incline up the driveway. The next morning I was able to start the car and take it to the Volvo dealer. All along the trip the felt like it was going to stall any minute. I kept a constant speed and did not take any chances with sudden acceleration or passing. After the dealer service department looked at the car I was informed that the throttle assembly needed to be replaced. The repair cost me $1004. 52. (I kept the repair invoice) the car had 56157 miles on it and had just come off the manufacturers warranty. I called Volvo north America to complain and they said somebody would get back to me. I then got a call from the dealer. Apparently Volvo passed the buck the dealer and all they told me was that they simply repaired my car. After reading about your probe of Volvo cars specific to the kind of problem we had I decided to file a complaint.