If you're traveling in a vehicle that is moving at the speed of light, what happens when you turn on the headlights?
Only light can travel at the speed of light. So either the vehicle turned into light or it can not reach the speed of light.
To the observer who is moving with vehicle they behave exactly the same as if the vehicle was still. The speed of light is independent of the motion of the source or observer.
Because you have mass you couldn't achieve the speed of light so let's just say 99% instead. But actually it isn't 99% of the speed of light and that's it, it has to be 99% the speed of light with respect to something else. This is because there is no absolute reference frame of positions in the universe, everything only has a position and speed relative to other objects. So here you are, travelling toward me with a relative speed of 99% the speed of light and you turn a light on. I see the light come toward me at the speed of light with respect to me, you see it move away at the speed of light with respect to you (obv we don't see it, but we can do experiments to measure it). And the reason this can happen it that due to our relative speed we have completely different views about distances and times. This isn't an explanation but of why or how but just enough to see that there is a way out.
Basically, the light will be traveling at the same speed as you. Therefore, it will not reach an observers eyes before the vehicle does straight on. In this situation, an observer would not be able to see you until you hit them or passed them. From the side, observers would be able to see the lights turn on, although at a slightly delayed time.
The light bunches up at the headlights. Note that this is not possible in a vacuum because nothing with mass can travel that fast. But it is theoretically possible in a medium, because the medium reduces the speed of light. Update: Paul Jackson's answer is also correct.
