Physics quiz question: accelerating car

Physics 205A Quiz 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 2.57(a)

[3.0 points.] Consider a car traveling in the +x direction that accelerates uniformly from a speed of 15 m/s to 22 m/s in a time of 12 s. How far did the car travel during this time?
(A) 84 m.
(B) 180 m.
(C) 222 m.
(D) 264 m.

Correct answer: (C)

The displacement (straight-line distance traveled) by the car is the area under a v_x(t) graph, which in this case is a trapezoid, with heights v_ix = 15 m/s and v_if = 22 m/s, and base delta(t) = 12 s, such that the total area can either be expressed as (1/2)*(v_ix + v_if)*delta(t), or "rectangle and triangle" v_ix*delta(t) + (1/2)*(v_fx - v_ix)*delta(t).

Response (D) is the distance traveled by the car if it had a speed of 22 m/s for the entire 12 s, while response (B) is the distance traveled by the car if it had a speed of 15 m/s for the entire 12 s. Response (A) is the difference between response (D) and the correct response (C).

Student responses
Sections 30880, 30881
(A) : 8 students
(B) : 0 students
(C) : 38 students
(D) : 2 students

"Difficulty level": 79%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.40