According to Einstein's theory of relativity, nothing can travel faster than light. If a car could somehow reach light speed, time would stop for the objects inside. Thus, turning on headlights wouldn't work, as photons from the light can't exceed the speed of light. This scenario is purely hypothetical, as current physics deems it impossible.
According to the theory of relativity, you can't travel at the speed of light. So the question is based on a hypothetical situation that can't actually occur.
According to Einstein's theory of relativity, no object with mass can reach the speed of light. But hypothetically, if you could travel at light speed, time would stop for you and distances would contract to zero. From your perspective, turning on the headlights wouldn't produce a visible beam, as light can't move faster than itself. To an outside observer, the light would still travel at light speed due to the constancy of the speed of light in all reference frames.
According to Einstein's Special Relativity, a massive object like a car cannot reach the speed of light as it would require infinite energy.
However, if you were traveling very close to it (e.g., 99.9% $c$), the light would still move away from you at the speed of light ($c$) from your perspective. The speed of light is constant for all observers. An outside observer would see the light beam moving at $c$ and your car moving just slightly slower than the beam.
At the speed of light, this scenario is physically impossible for a car (or any object with mass), as it would require infinite energy.
However, in the spirit of the thought experiment: according to relativity, light always travels at c relative to any observer. So if you could somehow reach light speed, you'd still see your headlight beams moving away from you at the speed of light. There's no "adding" speeds—light's speed is constant for all observers.
In relativity, a car with mass can’t reach the speed of light. But imagine you could: in your own frame you’re always “at rest,” so your headlights would work normally and light would move away from you at light speed. The paradox comes from assuming a massive object can actually go at light speed.
If you're in a car traveling at the speed of light (which is impossible for objects with mass), turning on the headlights wouldn't change anything—light would still travel at c (the speed of light) relative to you, but from an outside observer's perspective, time for you would appear frozen (due to relativity).
In reality, no massive object can reach c, but if you approached it, the light would still move ahead of you at c in all frames of reference.
Nothing would happen because no object with mass can reach light speed. Only massless particles like photons travel at c. The scenario is impossible within known physics.
According to relativity, you cannot travel at light speed. For an observer watching you approach it, your headlights' light would still be measured as moving away from you at the speed of light.