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, and always points in the same direction as his velocity. 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