20081012

Physics midterm question: constant velocity, straight-line trajectory?

Physics 205A Midterm 1, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 3.8

[10 points.] If an object is traveling at constant velocity, discuss whether or not it is necessarily traveling in a straight line. Explain your reasoning using the properties of velocity and acceleration vectors.

Solution and grading rubric:
  • p = 10/10:
    Correct. Recognizes that constant velocity has constant speed and direction; or that acceleration must be zero; or displacement must be changing at a constant rate; or that Newton's first law must apply in order that the object must be traveling in a straight line (at constant speed). May instead argue that a stationary object has a constant velocity (of zero!), but does not move in a straight line.
  • r = 8/10:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May interpret problem as asking about average velocity, in which case uniform circular motion would have a constant average velocity, if the time interval is the same as the period of revolution.
  • t = 6/10:
    Nearly correct, but argument has conceptual errors, or is incomplete.
  • v = 4/10:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  • x = 2/10:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y = 1/10:
    Irrelevant discussion/effectively blank.
  • z = 0/10:
    Blank.

Grading distribution:
Sections 70854, 70855
p: 20 students
r: 6 students
t: 2 students
v: 13 students
x: 4 students
y: 0 students
z: 0 students

A sample of a "p" response (from student 5880) where the stationary case is argued:
An "r" response (from student 7220) who reinterprets the question as referring to average velocity:

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