20080328

Physics midterm question: distance traveled vs. displacement magnitude

Physics 5A (currently Physics 205A) Midterm 1, spring semester 2008
Cuesta College, San Luis Obispo, CA

Could the distance traveled and the magnitude of displacement be different when describing the same motion of an object? Explain your reasoning using an example and discussion of the properties of position, distance traveled, and displacement.

Solution and grading rubric:
  • p:
    Correct. Draws a diagram and/or makes a convincing argument that demonstrates that the distance traveled is the "actual winding path" taken from a start position to a finish position, while the magnitude of displacement is the "straight line distance" from start to finish, and can be quite different if an object makes a non-linear trajectory.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have some ambiguity concerning displacement or magnitude of displacement, but otherwise makes correct distinction between distance traveled and displacement (magnitude) using an example.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. Argument mainly based on difference between a scalar and a vector property, i.e., comparison of distance traveled and displacement (as opposed to displacement magnitude).
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May involve velocities, forces, and/or net forces.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.

Grading distribution:
p: 29 students
r: 5 students
t: 4 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 7667) is shown below, using an example of commuting to/from Cuesta College between parking and re-parking a car:
Another "p" response (from student 7137) is shown below, with an illustrated example:

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