Physics final exam question: average speed greater than average velocity magnitude?

Physics 205A Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 2.1, 2.2, 3.9

A Physics 205A student kicks a ball off the edge of a cliff with an initial velocity that is directed 45° below the horizontal, and the ball hits the ground below 3.0 s later. Discuss why the average speed of the ball will be greater than the magnitude of the average velocity as it falls to the ground. Explain your reasoning using the properties of distance traveled, displacement, and elapsed time.

Solution and grading rubric:

• p:
  Correct. Understands distinction between average speed (distance traveled divided by elapsed time) and magnitude of average velocity (magnitude of displacement divided by elapsed time), and clearly indicates how the distance traveled by the ball is greater than the magnitude of displacement during its trajectory towards the ground.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Does not explicitly discuss how distance traveled is greater than the magnitude of displacement for this trajectory (as most generally it is possible for the distance traveled to be equal to the magnitude of the displacement).
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least distinguishes between distance traveled and magnitude of displacement.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on some other aspect of kinematics, vectors, and differential calculus.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion based on concepts other than kinematics, vectors, and differential calculus.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalPr0p
p: 20 students
r: 8 students
t: 11 students
v: 11 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 3003):