If time stops at the speed of light, you wouldn't be able to go faster than the speed of light, since the only way to enter time again would be to go slower than the speed of light... If time doesn't rewind at higher velocities, but higher velocities require more than infinite energy, which is impossible to obtain.
If you walk on a spaceship, you move relative to the spaceship, I think there's some relativity in this which will answer the question.
Here's a video I would recommend everyone to watch if they're curious about the strange things happening about the speed of light: