At launch, most rockets accelerate very quickly, reaching speeds of several hundred miles per hour within seconds. For example, the Space Shuttle would accelerate from 0 to about 1,700 mph (2,700 km/h) in just under two minutes, while the Falcon 9 rocket could reach speeds of over 4,500 mph (7,200 km/h) in under ten seconds. These initial acceleration stages are powered by the rocket's main engines.
Once the initial acceleration is complete, the rocket will continue to accelerate at a slower rate as it rises in altitude and burns through its fuel. The Saturn V rocket used for the Apollo moon missions, for instance, would eventually reach speeds of around 25,000 mph (40,000 km/h) as it continued its journey towards the Moon.
It's important to note that these speeds are relative to Earth's surface, and not necessarily the rocket's speed in space. In space, the rocket's motion would instead be measured relative to other objects in the solar system, such as the sun or other planets.
