A quick calculation indicates that, if the moon were to stop dead in its orbit (not taking into account the negligible air resistance it would meet shortly before impact), classical physics says it would accelerate towards Earth at nearly 33 m/s/s, reaching a speed at impact of roughly 5025 m/s. That is 18,090 km/h, or 11,241 mph.
However General Relativity tells us that the Moon is in fact falling towards Earth with the same potential energy, but the Earth’s gravitational field has warped space-time such that the Moon appears to orbit the Earth. It doesn’t trace an elliptical path as such, but falls towards Earth in a straight line through space-time that is warped in an elliptical fashion.