Why would my car out of the blue have no acceleration? No warning.

I had this happen to me also . It followed up with the car not starting at all and had to have it towed home. What my problem turned out to be was not enough electrical power was being generated by the alternator to the battery which in turn made the car not accelerate to the point that it would only go maybe 5 miles an hour before it died completely. Replaced both battery and alternator and everything works fine now. Oh yes the the ignition switch locked up as well when this happened. Thought I had a major problem but I didn't.