In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by

where s is the distance in meters and t is the time to run that distance in seconds.

(a) Find Kennelly’s estimate for the fastest mile.
(b) Find dt/ds when s = 100 and interpret your answer.
(c) Compare this and other estimates to the current world records. Have these estimates been surpassed?

Transcribed Image Text:

t = 0.0588s¹.125