Firstly, such questions cannot have a definite answer because it is completely hypothetical.
If you do travel at a speed more than the speed of light (hypothetically), you'd be just energy, with no mass whatsoever.
Suppose that this does not happen, then when you turn on your headlights, you may not see the light due to extreme Doppler shift in frequencies.
As you are in space, if the light does not fall on anything, you'll simply see darkness ahead, regardless of your headlights. (You see light ahead of you due to headlights because they fall on the road). So it could be either of these possibilities. What would be your solution?

nothing in the universe can move faster than light(another rule!).just like you can't imagine a male giving birth(excluding transgenders),you can't take anything run faster than light.but you may think about this-what happens to the sound of supersonic jets?

Its a paradox

@Ragib, in super-sonic jets, when it passes through the air, the change in pressure is such, the the sound waves are compressed together, as they have no where to go, and then suddenly release/expand into the air with such force, that they create an explosion of sorts, which is called a sonic boom. Am I right?

want us to think about relative speeds?then,when reflected,you will see the light.because the light source will always move at speed of car.

actually,i didn't think about the ques very much before asking it.but i think you are right.there sound of course move with the jet at same speed.