During a 100 m sprint, Usain Bolt reaches his maximum speed in 2 seconds from re

Question

During a 100 m sprint, Usain Bolt reaches his maximum speed in 2 seconds from rest with constant acceleration. He then maintains this maximum speed until he reaches the 90 m mark, when he peeks back and sees that the other sprinters in the race are all left in his wake. He then decides to start showboating again by reducing his speed at a constant rate, as he did in the 2008 Olympics, until he crosses the finish line at a speed of 9 m/s. If Usain Bolt finishes his race in 9.6 seconds, determine his maximum speed during the race.

Explanation / Answer

Given:
Total displacement , S = 100 m
Acceleration in the beginning = A m/s2
Deceleration at the end = D m/s2
Uniform velocity during the sprint =U m/s
Time taken, T = 9.6 s

Time during last deceleration,= t s (Please do not confuse with the t in the formulas )

Solution:

Note: Formulas are represented by small letters and problem variables by capital letters.

At the end of race

92 = U2 - 2xDx10 { using this equation of motion v2 = u2 + 2as}

81 = U2 - 20D...........................(1)

9 = U - Dt...............................(2) { using this equation of motion v = u +at }

For the last stretch

10 = Ut - (1/2)Dt2..............................(3) { using this equation of motion s = ut + (1/2)at2 }

From (1) D= (U2-81)/20.............(4)

Substituting D in equation (2) and simplifying we get

9 = U - [(U2-81)/20]t and solving for t we get

t= 20/(U+9).........(5)

Substituting for D and t in (3) we get after simplification

U2 - 20U + 99 = 0

Solving for U we get, U= 9, 11 m/s

U cannot be 9 m/s since it would yield meaningless result when substituted in (4)

U = 11 m/s

The maximum velocity is the during the constant velocity run , which is U

U = 11 m/s

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