Physics quiz question: BMW 328i versus Cadillac ATS

Physics 205A Quiz 4, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.71

A 2013 BMW 328i (mass 1,545 kg) takes 7.7 s to accelerate from 22 m/s to 31 m/s on a horizontal track, while a 2013 Cadillac ATS (mass 1,577 kg) takes 8.6 sec to do so(*). Which car's engine has the greater average mechanical power output? Ignore friction and drag.
(A) BMW 328i.
(B) Cadillac ATS.
(C) (There is a tie.)
(D) (Not enough information is given.)

(*) Source: "BMW 328i curb weight: 3390 pounds, top gear, 50-70 mph: 7.7 sec; Cadillac ATS curb weight 3477 pounds, top gear, 50-70 mph: 8.6 sec," http://media.caranddriver.com/files/2013-bmw-328i-vs-2013-cadillac-ats2013-cadillac-ats-and-2013-bmw-328i-comparo.pdf.

Correct answer: (A)

The mechanical output of the cars' engines does non-conservative work to increase translational kinetic energy:

Wnc = ∆K,

where the average power output of the cars' engines is the rate of work done per time:

Pav = Wnc/∆t = ∆K/∆t.

For the BMW 328i, the engine power output is:

Pav = (1,545 kg)·((31 m/s)2 - (22 m/s)2)/(7.7 s) = 9.6×104 watts,

And for the Cadillac ATS, the engine power output is:

Pav = (1,577 kg)·((31 m/s)2 - (22 m/s)2)/(8.6 s) = 8.7×104 watts.

Thus the engine BMW 328i has the greater power output. (Note that the Cadillac ATS has the greater increase in kinetic energy, due to its greater mass, but will have a lower engine power output because of the longer time required for it to accelerate from 22 m/s to 31 m/s.)

Sections 70854, 70855
Exam code: quiz04Bmw3
(A) : 40 students
(B) : 10 students
(C) : 2 students
(D) : 0 students

Success level: 77%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33

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