Physics midterm question: distance traveled vs. displacement

Physics 205A Midterm 1, fall semester 2019
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of a Physics 205A student walking along a horizontal road is shown at right. The student started at x = 0 at t = 0. Discuss whether the magnitude of the distance traveled by the student is equal to or greater than the magnitude of the displacement. Explain your reasoning using the properties of velocity, position, time, distance traveled, and/or displacement.

Solution and grading rubric:

• p:
  Correct. Demonstrates that the distance traveled is equal to the magnitude of displacement, as the student always travels in the same (positive) direction (only positive horizontal velocity values), without reversing direction (no negative horizontal velocity values).
• 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. Conceptual understanding of displacement and distance traveled, but somehow misinterprets/misapplies/ignores the given information.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01duCk
p: 38 students
r: 0 students
t: 5 students
v: 4 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 5808):