Answer:
This very maneuver is performed by the Shuttle during every mission.
At launch, the Shuttle is on the ground, and then rises, and tilts to the east. The purpose of this particular path is twofold; first and foremost, to get above the vast majority of the atmosphere as quickly as possible, and second, to accelerate to something close to orbital speed. At the typical altitude that the Shuttle flies, this is about 18,000 miles per hour.
The engines can't run continually; they don't carry enough fuel. So they accelerate and then coast, on a ballistic trajectory that will bring them to just touch the altitude of the ISS. Then, just as they reach that altitude, they fire the main engines again to "circularize" the orbit.