Answer / Step-by-step explanation:
(1) Given t = 0.0588s ¹.¹²⁵
where s is the distance and t is the time to run that distance.
The second portion asks us to find the derivative of the equation when our s value is equal to 20 and interpret.
(2) First, we try to convert the unit from miles to meters
Therefore, 1 mile = 1609 meters
Then,
t = 0.0588 ( 1609 ) ¹.¹²⁵
=238 . 09
This gives us the instantaneous rate of change of seconds between every 20 meters ran.
The last portion asks us to compare this estimate to current world records. And have they been surpassed?
As of today, the fastest official record for a standard mile is held by a man from Morocco named Hichan El Guerrouj. The time was recorded at 3.43 minutes in Rome, Italy on July 7th, 1999.
Now, keep in mind that this is almost a full minute slower than the estimated time. However, how do these projections hold up against Usain Bolt, the man that is considered the fastest man in the world ?
Although, Usain Bolt does run long distances, he holds records in nearly every sprinting event that he has ever competed in.
Hence, Kennelly's estimate for the fastest mile is 238.09
(3) Now, noting that since dt / ds = 0.0588 ( 1.25 ) s ⁰.¹²⁵
Then,
dt / ds I 100 = 0.0588 (1.25) (20) ⁰.¹²⁵
= 0.1176
=