To attain escape velocity from Earth's atmosphere, the space shuttle must reach a speed of approximately 11.2 kilometers per second (km/s) or 7.0 miles per second (mi/s). This velocity is necessary to overcome the gravitational pull of the Earth and achieve an unbound trajectory into outer space.

Escape velocity is the minimum speed required for an object to break free of the gravitational attraction of a celestial body. It depends on the mass and radius of the body, and for Earth, it is approximately 11.2 km/s.

The space shuttle, or any spacecraft, achieves escape velocity through a combination of powerful rocket propulsion and careful trajectory planning. The rockets provide the necessary thrust to accelerate the spacecraft, while the trajectory ensures that the spacecraft is launched at an angle that allows it to break free of Earth's gravity and reach orbit or continue its journey into deep space.