Cuesta College, San Luis Obispo, CA
Can the average speed and the magnitude of the average velocity be equal? If so, give an example. If not, then discuss why not. Explain your reasoning by using the properties of position, distance traveled, displacement, velocity, and speed.
Solution and grading rubric:
- p:
Correct. Argues either case where they may be equal to each other (straight line travel with no reverse direction changes, or at rest); or argues that they cannot be equal (in general) for typically non-straight paths. - r:
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May confuse instantaneous with average quantities, or involve +/– directions when discussing magnitudes. - t:
Nearly correct, but argument has conceptual errors, or is incomplete. At least recognizes average speed is magnitude of average velocity, or that straight line travel is required, but may interpret "average" as adding multiple quantities and dividing by number of items. - v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. - x:
Implementation/application of ideas, but credit given for effort rather than merit. - y:
Irrelevant discussion/effectively blank. - z:
Blank.
Sections 30880, 30881
p: 9 students
r: 4 students
t: 16 students
v: 7 students
x: 2 students
y: 0 students
z: 1 student
A sample of a "p" response (from student 0506) with an example of straight-line travel, where average speed and the magnitude of average velocity would be equal:
Another sample "p" response (from student 4974) showing examples where average speed and the magnitude of average velocity would not be equal:
A sample "t" response (from student 4469) positing that average speed would be by definition the magnitude of the average velocity vector (which would only be true for the instantaneous speed and instantaneous velocity):
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