Physics quiz question: displacement from velocity versus time graph

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 2.11

[3.0 points.] Consider the v_x(t) graph of an object moving along a straight line, as shown at right. How far does the object move between t = 0 s and t = 8.0 s?
(A) 18 m.
(B) 25 m.
(C) 28 m.
(D) 35 m.

Correct answer: (B)

The displacement (straight-line distance traveled) by object is the area under a v_x(t) graph, which in this case is a trapezoid.

Response (C) is the distance traveled by the object if it had uniformly increased its speed from rest to 7.0 m/s for the entire 8.0 s; response (A) is the distance traveled by the object if it had uniformly increased its speed from rest to 7.0 m/s from 3.0 s to 8.0 s. Response (D) is the difference between the distance traveled by the object had it continuously traveling at 7.0 m/s for the entire 8.0 s, and the correct response (B).

Student responses
Sections 30880, 30881
(A) : 2 students
(B) : 39 students
(C) : 6 students
(D) : 1 student

"Difficulty level": 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.27