Cheetahs probably evolved as pronghorn antelope predators in Pliestocene NorAm, and it looks very much like there was a cheetah/pronghorn arms race for speed.
Why there was that arms race, and why there are cheetahs in Africa, are pretty interesting questions.
CMIIW, but isn't the African cheetah (Acinonyx) much better adapted for sprinting than the North American cheetah (Miracinonyx), which has a more puma-like build?
Hmm, the Wikipedia page (http://en.wikipedia.org/wiki/Miracinonyx) says that the running abilities in both genera were convergent. -- Mike Keesey