Jet fuel has variants, but a very common one is known as Jet A can be understood as lead-free kerosene, much closer in structure to diesel fuel. Hence, it can be used to fuel Turbine Engines as well as the Compression Engines. However, due to lack of lubrication properties, jet fuel will damage the engine.
The other factor to account for is the high heat content of the jet fuel and how car engines are not designed for it. Jet fuel wouldn’t vaporize very easily and not to mention how hard it would be to ignite using a spark ignition.
It would be analogical to using diesel in a petrol engine. Some engines might endure this combination of fuels for some time, followed by misfires and eventually coming to a halt. Due to heavy nature of the Jet fuel, it will damage the fuel pump and the engine at large.
According to Manuel Martinez-Sanchez, an aeronautics and astronautics professor at the Massachusetts Institute of Technology, the diesel engine might work using liquid Hydrogen. However, the temperature it requires is a staggering –432°F, hence the car engine would eventually freeze. Unfortunately, cars are not meant to go faster on Jet Fuel.
The street-legal jet cars are designed to support two separate engines, gasoline engine in front along with a jet engine in the back.
In conclusion, the car wouldn’t start in case of spark-ignition engines, wouldn’t run, and might catch fire. It might run for a small duration in case of diesel engines, but not without causing long-term damage.