Comets travel between 26 miles per second and 298 miles per second. The speed depends on two factors: the shape of its orbit and its proximity to the Sun at a particular point in time.
Kepler's laws explain the speeds of objects like comets that travel in elliptical orbits. In basic terms, the wider the orbit, the slower the speed. A more narrow orbit results in a higher speed. The speed of a comet also increases the closer it draws to the Sun. However, some researchers theorize that a comet approaching 300 miles per second would be thrown into a parabolic or hyperbolic orbit and end up ejected from the solar system.