The manual for Reach said the sprint module basically just disabled some inhibitors and safety measures, and I think helped with cooling(?). I imagine they'd explain the speed boosts similarly. After all, Spartans are supposed to be capable of lightning-quick movement, and there must be some reason they don't employ that constantly (gameplay explains a lot but not everything). At least one of the new armor pieces talks about pushing the capabilities of the cybernetics in Spartans too, to the point where the ethics of it are questionable.