20120919

Physics quiz question: Usain Bolt 100 m sprint

Physics 205A Quiz 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

"Leichtathletik WM 2009 Berlin"
André Zehetbauer
flic.kr/p/6RmNQn

Jamaican sprinter Usain Bolt[*] holds the world record for the 100 m sprint, covering that (straight-line) distance in 9.58 s in Berlin, 2009. Assume that his acceleration starting from rest to when he crosses the finish line is constant. During this race, the magnitude of his acceleration was:
(A) 1.09 m/s2.
(B) 2.18 m/s2.
(C) 10.4 m/s2.
(D) 20.9 m/s2.

[*] wki.pe/Usain_Bolt.

Correct answer (highlight to unhide): (B)

The following quantities are given (or assumed to be known):

(x0= 0 m),
(t0= 0 s),
x= +100 m,
t = 9.58 s,
v0x = 0.

So in the equations for constant acceleration motion in the horizontal direction, the following quantities are unknown, or are to be explicitly solved for:

vx = v0x + ax·t,

x = (1/2)·(vx + v0xt,

x = v0x·t + (1/2)·ax·(t)2,

vx2 = v0x2 + 2·ax·x.

With the unknown quantity ax to be solved for appearing in the third equation, with all other quantities given (or assumed to be known), then:

(1/2)·ax·(t)2 = xv0x·t,

ax = 2·x/(t)2 − 2·v0x/t,

ax = 2·(+100 m)/(9.58 s)2 − 2·(0)/(9.58 s) = +2.17920947 m/s2,

or to three significant figures (which follows from the three significant figures in 9.58 s, and assuming that the 100 m distance must be exact (or presumably measured with more precision than to the nearest meter!)), the acceleration has a magnitude of 2.18 m/s2.

(Response (A) is x/(t)2; response (C) is x/t; response (D) is 2·x/t.)

Sections 70854, 70855
Exam code: quiz02Bo74
(A) : 18 students
(B) : 23 students
(C) : 6 students
(D) : 1 student

Success level: 40%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.57

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