The speed the person would measure for the light coming from the car's headlights is 300,000 km/s.
According to Einstein's theory of relativity published in 1905, the speed of light is constant irrespectively of the inertial frame in which it is measured. That is, the speed of light is constant irrespective of the motion of the source.
So, the speed of light coming from the headlights would not change.
So, the speed the person would measure for the light coming from the car's headlights is 300,000 km/s.
Learn more about Einstein's theory of relativity here:
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