Probably the most productive thing a person could do for him/herself in 24 hours is an ultramarathon. Given 24 hours, I think most people could run (or at least walk) 100 miles. The physical improvement from only one day of exercise, no matter how strenuous, will of course be small. Mentally though, it would show a person exactly what they're capable of- anything. Proving that to one's self beyond doubt would definitely be worth the time and resulting injury.
