I think the car of the future will look and function much like todays cars, only a lot more efficiently. The size of a car doesn’t seem to have changed all that much since the early days. Compare a model A to a 55 Chevy to a new Malibu. The Malibu is faster and gets much better gas mileage than the 55 Belair, and the Belair was faster and got better mileage that the Model A (but not much better).
I think in the near future, you will see a computer controlled valve event engine, that is the valves will be opened by a solenoid or a hydraulic system controlled by the computer, not a cam. That would give cars the kind of boost that fuel injection gave over carburetors.
Later, I think that fuel cells will be the next solution. But for that, we will need nuclear power plants that can be used to make hydrogen during off peak hours. Wind farms may also be able to provide some of the hydrogen also during off peak hours. Ultimately I would hope that we develop fusion power generators to replace the fission powered generators of today, but thats another topic.
I don’t expect cars of the future to go much faster than todays cars, I think we have hit the human speed limit on the ground. Our eyes have a flicker rate of about 30 times/sec which limits our reaction speed. Maybe some automated drive system might allow higher speeds, but if we are in control, speeds will be about the same.