If you stretched a razor-sharp titanium wire across the highway, would a speeding car get chopped in half?

Assuming that the wire is incredibly strong (titanium) and incredibly well secured at both ends, would a speeding car get chopped in half upon colliding with the razor-sharp, razor-thin, super-strong wire? What if a jogger ran through it? Would it chop the jogger in half? I'm not planning on doing this, so please don't think I'm a psycho. I'm just curious.