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:

W_nc = ∆K,

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

P_av = W_nc/∆t = ∆K/∆t.

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

P_av = (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:

P_av = (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