20080829

Physics clicker question: instantaneous speed vs. magnitude of instantaneous velocity

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

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the middle of their learning cycle, after discussing the distinction between average and instantaneous quantities.

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

Sections 70854, 70855
(A) : 1 student
(B) : 1 student
(C) : 16 students
(D) : 27 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) : 0 students
(B) : 0 student
(C) : 25 students
(D) : 20 students
(E) : 0 students

Correct answer: (C)

While not an overwhelming number of correct responses, at least an appreciable shift away from (D), which is an incorrect answer, a point brought up in the whole-class discussion after the second pass.

Instantaneous quantities are evaluated in the limit that the elapsed time interval approaches zero. From a previous discussion in class, average speeds can be greater than the magnitude of average velocities when the trajectory between the initial and final positions doubles back and forth on itself, but instantaneous speeds must be the same as the magnitudes of instantaneous velocities, because in the limit that the elapsed time interval approaches zero, there can be only straight-line travel with no "back-and-forth" between initial and final positions.

In the follow-up discussion, a student asked whether instantaneous speeds can still be greater than magnitudes of instantaneous velocities for something very small, say, like molecules. But even though the brownian motion of molecules would jostle it back and forth over small distances, the nature of the time interval for instantaneous quantities means that it should be made sufficiently small enough that there is no "back-and-forth" between initial and final positions.

20080827

Erasing slate: wow!

"Wow!" by Anonymous
August 25, 2008
Cuesta College, San Luis Obispo, CA

Latest scribbling on the lift-and-erase slate in the hallway, outside the office door.

20080826

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!

20080822

FCI pre-test comparison: Cuesta College versus UC-Davis

Students at both Cuesta College (San Luis Obispo, CA) and the University of California at Davis were administered the Force Concept Inventory (Doug Hestenes, et al.) during the first week of instruction.

Cuesta College UC-Davis
Physics 205A Physics 7B
Fall Semester Summer Session II
2008 2002
N 53 students 76 students
low 4 2
mean 10.8 +/- 4.9 9.1 +/- 4.3
high 24 27

A "Student" t-test of the null hypothesis results in p = 0.0206, thus there is a significant difference between Cuesta College and UC-Davis FCI pre-test scores.

Apparently this semester at Cuesta College, students are slightly more knowledgeable about the Newtonian physics concepts covered in the FCI as UC-Davis students at the start of introductory college physics, at a statistically significant level.

Later this semester (Fall 2008), a comparison will be made between Cuesta College and UC-Davis FCI post-tests, along with their pre- to post-test gains.

D. Hestenes, M. Wells, and G. Swackhamer, Arizona State University, "Force Concept Inventory," Phys. Teach. 30, 141-158 (1992).
Development of the FCI, a 30-question survey of basic Newtonian mechanics concepts.

Previous FCI results:

20080820

Discovering real and virtual images

080724-1040074
http://www.flickr.com/photos/waiferx/2766109677/
Originally uploaded by Waifer X

Discovering a real image and a virtual image from a concave mirror. Reuben H. Fleet Science Center, San Diego, CA.

20080817

Erasing slate: once upon a time...

"Once Upon A Time..." by Anonymous
Summer Break 2008
Cuesta College, San Luis Obispo, CA

Latest scribbling on the lift-and-erase slate in the hallway, outside the office door. Appropriately enough, just before the start of fall semester.

20080816

Stop, look, wave

080803-1040633
http://www.flickr.com/photos/waiferx/2743852851/
Originally uploaded by Waifer X

Stop, look...and don't forget to wave, kids! Crosswalk, San Bruno, CA.

20080815

Found physics: dapples of sunlight

080731-1040621
http://www.flickr.com/photos/waiferx/2721860968/
Originally uploaded by Waifer X

Dapples of sunlight; built up from many pinhole images of the sun through tree leaves and branches.

20080814

Heat transfer modes: radiation, convection, and conduction

080731-1040630
http://www.flickr.com/photos/waiferx/2721036539/
Originally uploaded by Waifer X

The three modes of heat transfer: radiation, convection, and conduction.