There is no air resistance out in space and the force of Earth's gravity is weaker (rockets are typically fired upwards against the pull of gravity), so in general, a rocket can accelerate faster and reach higher speeds. read more
A rocket starts at rest from ground. When it drops its payload at say, a geostationary orbit, its speed will be about 3 km/s. Obviously, its speed has been increasing from zero to this value as it got higher. So, a rocket is faster in space than in earth. read more
Rockets and engines in space behave according to Isaac Newton's third law of motion: Every action produces an equal and opposite reaction. When a rocketshoots fuel out one end, this propels the rocket forward — no air is required. read more
The main objective of the rocket engine is not only to get the cargo above the atmosphere, but more importantly to accelerate it in horizontal direction to the orbital speed (7.5 km/s for the orbital altitudes of the Shuttle and International Space Station). read more