Physics clicker question: distance traveled vs. displacement magnitude

Physics 205A, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 2.1 (extended)

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning of their learning cycle:

In general, which statement(s) is/are possible?
(A) Distance traveled > magnitude of displacement.
(B) Distance traveled < magnitude of displacement.
(C) Distance traveled = magnitude of displacement.
(D) (More than one of the above choices.)
(E) (I'm lost, and don't know how to answer this.)

Sections 70854, 70855
(A) : 11 students
(B) : 5 students
(C) : 9 students
(D) : 17 students
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Sections 70854, 70855
(A) : 5 students
(B) : 1 student
(C) : 1 student
(D) : 37 students
(E) : 0 students

Correct answer: (D)

If an object moves along one dimension such that it does not retrace its path, then the distance traveled from its initial location to its final location is exactly equal to the magnitude of the displacement (the straight-line vector that points from the initial to final location), so choice (C) is possible. However, if an object moves back-and-forth along one dimension, then the distance traveled will be longer than the magnitude of the displacement, so in this case choice (A) is possible. Under no circumstances would (B) be possible. Never. Never? Never-ever-ever!