I am using the BattleTech universe for my stories, which has nuclear fusion powered cars. My assumption is that they work similarly to an EV, but with an onboard power plant. So, they'd still be run by electrical traction motors, and have a battery to provide juice to start the reactor up and run small accessories. The reactor would work in much the same way that a power plant does, using heat to generate steam that drives electrical dynamos.
So, I hop into my Rotunda and press the start button. I think I'd be hearing the humming of the reactor's magnetic containment, the rumble of the reactor coolant pumps, and perhaps the whining of the steam turbines as well. The instrument cluster looks similar to that of a 21st century car, but has some additional gauges like temperature gauges for the reactor and the drive motor coolant. The speedometer still works the same, but the RPM gauge instead watches the dynamo turbine's speed. I'd have the same instant torque that an EV has, and more then enough horsepower to go around.
One thing that I'm still trying to figure out is the fuel--from BattleTech, a fusion reactor in a BattleMech is used in much the same way to generate power, and is efficient enough that it only has to be refueled very infrequently, about once every few decades or so. The game states that coolant wears out and has to be replaced much more frequently, so would coolant top-off and refresh stations become the new gas station?
Other then that, there may be many more things I haven't though of, so tell me your thoughts below--what experiences, costs, and maintenance procedures would come with owning a nuclear car?