There are different kinds of rockets, and they have varying speeds. However, a conventional rocket needs to travel at least 4.9 miles per second, or about 17,000 mph, to reach space at low Earth orbit, claims Redshift Live.
Rockets are not build to go as fast as possible; they are built to meet the minimum speeds necessary to achieve their goals. Hence, the speed of a rocket depends on where it is going. For instance, a rocket needs to travel at least 24,200 mph to escape Earth's orbit, and at least 25,700 mph to reach lunar orbit, according to Northwestern University.