The moon rotates at a constant speed, but orbits at various speeds depending on how close it is to the earth. The closer it is the faster it travels. For the sake of this question it is about 1.03 km/sec. At these speeds a full orbit around the earth takes about 27.3 days.
At the apogee of its orbit, the moon is traveling its slowest with a speed of 3454.5km/hr. At the perigee of its orbit the moon is traveling its fastest at 3896.9 km/hr.
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