If an object or particle were to travel faster than the speed of light, how would I measure it? How would I measure the speed of particle hypothetically traveling faster than light?
Is there any kind of camera that could detect this?
 A: One would literally just measure the speed of this particle the same as you'd measure the speed of any other particle. It's change in distance over change in time. (This is all theoretical, obviously, because particles don't travel faster than the speed of light.)
Interestingly enough, there is a camera. At a trillion frames per second, it can watch light moving. The camera was built by MIT's media lab. They call it femto-photography. The leader of the team, Ramesh Raskar, gave a TED talk, which includes a video of the camera at work. It's really interesting - watch it here.
A: I don't think you could. I see this as a problem of resolution. Just as we can't know for a fact that electrons are fundamental, we can't see anything smaller than an electron because an electron is the smallest thing we know of that we can use to 'see' small things, we can't really know for certain that nothing can travel faster than light, since light is the fastest thing we know of that we can use to 'see' a thing. We don't really see the thing, just it's interactions with things around it whether that be via light waves, or sound waves, or whatever.
If we were blind, and could only sense things by sound, or sonar, would we know that there are things that travel faster than sound? Our senses would tell us no. Even the sound waves from a supersonic jet only travel at the speed of sound. We need something much faster than an object whose speed is being measured in order to measure that object's speed.
And that fast camera? Even though it can show light moving, is sensitive only to the light wave which has as an upper limit the speed of light, so it would only be able to confirm that light moves at the speed of light.
