Physics midterm question: comparing distances traveled

Physics 205A Midterm 1, fall semester 2017
Cuesta College, San Luis Obispo, CA

The x(t) graph of a Physics 205A student walking along a straight line is shown at right. The student started at x = 0 at t = 0. Discuss why the student traveled a farther distance from t = 0 to t = 7 s than the distance traveled from t = 7 s to t = 10 s. Explain your reasoning using the properties of position, distance traveled, and displacement.

Solution and grading rubric:
  • p:
    Correct. Supports claim that student traveled a farther distance from t = 0 to t = 7 s than from t = 7 s to t = 10 s by discussing:
    1. distance traveled counts both forwards and backwards motion, such that from t = 0 to t = 7 s the student traveled a total distance of 3 m (2 m in the forwards direction, then 1 m in the backwards direction); compared to
    2. the distance traveled by the student from t = 7 s to t = 10 s is 2 m (always in the forward direction).
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. At least discussion demonstrates general understanding of distinction between distance traveled and displacement, but does not compare differences in distances traveled for the two time intervals.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May compare areas, slopes, elapsed times, average speeds and/or average velocities.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855
Exam code: midterm01mOoL
p: 25 students
r: 3 students
t: 10 students
v: 15 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2030):

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