The other day, I was in a rush to go some place. I turned on the car, put it in reverse and pushed the gas all the way done, instead of delivering power and going back faster, the RPM hit 2000 and went alllll the way done to about 600 rpm or 800 rpm. Then, I let go of the pedal, and hit it again, samething happened. The third time I pressed the gas in the beginning a little bit and then halfway down, the friggin car practically jumped, it gave me what i wanted. Also the same thing happened when I got out of the reverse and put it in drive!! WTF is wrong with this car. Also, a lot of times now, when i turn it on, it stays on for 5 seconds, and turns right back off!!!!

WTF is happening here?!?!?!
it's a 2002 Toyota Corolla LE, and yes, it just turns right back off a lot of times recently even though i dont touch anything. I just turn it on, and 5 seconds later, it just "dies". But the car still runs, later when I do it.