Physics midterm question: comparing average speed of two cars

Physics 205A Midterm 1, fall semester 2015
Cuesta College, San Luis Obispo, CA

The x(t) graph of two cars is shown at right. Discuss why both cars have the same average speed from t = 0 to t = 8 s. Explain your reasoning by using the properties of position, distance traveled, displacement, velocity, speed, and/or acceleration.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates either of two arguments:
  1. average speed is the distance traveled over the elapsed time, since both cars travel 6 m (either directly over the 8 s elapsed time; or 3 m during 0 < t < 2 s, then another 3 m during 6 s < t < 8 s); or
  2. the average velocity (displacement over elapsed time, (x – x₀)/(t – t₀) is the same for both cars, as they have the same initial and final locations at the starting and ending times, and the magnitude of the average velocity is equal to the average speed because both cars did not reverse direction.
• 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 (1) stated average speed = displacement/elapsed time and used endpoints instead of distance traveled, or (2) did not explicitly discuss how car 2 did not reverse direction in order for the average velocity magnitude to be equal the average speed.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. May involve finding the area under each graph.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01j0r6
p: 36 students
r: 23 students
t: 5 students
v: 14 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4815):