Physics clicker question: average acceleration from initial and final velocity vectors

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 3.41

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

Suppose a car travels one-quarter around a circle in a time of 1.0 s at a constant speed of 31.4 m/s, as shown at right.

Which red vector is delta(v) = v_f - v_i for this 1.0 s time interval?



Sections 30880, 30881
(A) : 18 students
(B) : 20 students
(C) : 1 student
(D) : 2 students
(E) : 1 student

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 30880, 30881
(A) : 10 students
(B) : 32 students
(C) : 0 students
(D) : 2 students
(E) : 0 students

Correct answer: (B)

The vector operation v_f - v_i can be interpreted as tail-to-head vector addition if the direction of v_i is reversed, such that delta(v) = v_f + (-v_i).

Pre- to post- peer-interaction gains:
pre-interaction correct = 48%
post-interaction correct = 73%
Hake, or normalized gain = 48%

Subsequently, students were asked to submit numerical answers to the following clicker question:

Note: a_av = delta(v)/delta(t) = (v_f - v_i)/delta(t).

The average acceleration magnitude of the car for this one-quarter around trip is _____ m/s^2.

Sections 30880, 30881
"-5" : 1 student
"-1.75" : 1 student
"-1" : 2 students
"0" : 19 students
"2" : 3 students
"4" : 1 student
"7.85" : 1 student
"8" : 2 students
"31.4" : 9 students
"44.4" : 2 students

Correct response: 44.4 m/s^2.

Due to too few students being able to answer this correctly, this question was not asked again for peer discussion. Instead, the instructor facilitated a whole-class discussion to determine why students chose certain answers.

"0" m/s^2 was chosen because the speed of the car was constant. However, the direction is changing, and this by itself requires a non-zero acceleration.

"2," "4," "7.85" and "8" m/s^2 were probably chosen due to reading the graph scales figuratively (even though no such scale was given).

"-1" m/s^2 was chosen because it was the "slope" of the a_av vector, thus confusing vector operations with kinematic graphs.

The length of the resultant delta(v) vector is 44.4 m/s (from applying the Pythagorean theorem), and thus a_av = delta(v)/delta(t) = 44.4 m/s^2.