The problem is that is very expensive, needs specially train crew to manage them, and need to be disposed of with a car when you decommission the carrier.
The advantage is they can provide a lot of power for a very long time duration so carriers can move at high-speed years without the need to refuel. On a submarine, the advantage is even larger because not oxygen and fuel is used and no exhaust is produced so you can stay underwater until you run out of food. You can make oxygen from seawater for the crew.
The US only uses nuclear power on carriers and submarines. They did have nuclear power cruisers before but they were to expensive to operate. That tells you something about the feasibility of a car. A few nuclear-powered cargo ships have been tested, but the have been too expensive to operate.
Nuclear power work by heating up water to steam and ut it on a gas turbine. The water then needs to be cooled or replaced with new water. Nuclear power is steam power with a different type of heat source. Add to that you need shielding around the reactor to protect humans from the radiation. Reactors need to be cooled after you use them we talk about active water cooling for weeks for nuclear power plants. The water pump needs an external energy source
Cars are often in accidents and you do not what to break apart and leak out radioactive material. You transport spent nuclear fuel in a container like https://bloximages.chicago2.vip.townnews.com/journalstar.com/content/tncms/assets/v3/editorial/d/67/d6729e0b-0652-553f-9634-12efb2dd3353/d6729e0b-0652-553f-9634-12efb2dd3353.image.jpg that do not break in a crash or a fire. You do not transport fuel that has just been used in a reactor, you keep it in spent fuel pools for a couple of years so the amount of heat they generate from nuclear decay is refused.
So a nuclear reactor in a car is a terrible idea. You can use energy from nuclear reactors to power a car. Generate electricity or perhaps hydrogen in a stationary power plane and use it to power a car.
So nuclear reactor on something that moves will be for ships and just a few types of military vessels. There are some nuclear ice breaks but I do not think they are really cost-efficient. Nuclear power also possible for space ships to move out in space. But that is where it is a good idea.
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