I was in a parking lot and came to a stop and placed the car in reverse to back into a parking space. The back-up camera was on and I began to back into the parking space when the car suddenly lurched/jerked forward and accelerated on its own. The car jumped the parking lot median strip and I hit a tree head on. I had my seatbelt on and the airbag deployed. The car then reversed back off the median into the parking lot. I turned off the car. Insurance company will have it inspected. The vehicle is a total loss. I was injured with a large lower abdomen hematoma and airbag burns on arms, wrists, and chest as well as various bruising. I was fortunate to have not hit pedestrians who were walking in the lot or other vehicles that were parked in the lot. There were no warning lights, messages, sounds. The brake assist did not engage. It was frightening.