Physics quiz question: semicircular path car

Physics 205A Quiz 3, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 3.32

[3.0 points.] Consider a car that travels halfway around a circle of radius 30 m in a time of 4.5 s at a constant speed. The initial velocity is in the –x direction and the final velocity is in the +x direction. What is the magnitude of the average velocity during these 4.5 s?
(A) 0 m/s.
(B) 6.7 m/s.
(C) 13 m/s.
(D) 21 m/s.

Correct answer: (C)

The definition of average velocity is displacement over time, of which displacement is the straight-line vector from the initial location to final location. In this case, the magnitude of the displacement is the diameter of the circle:

|v_ave| = |delta_r|/delta_t = diameter/delta_t.

Response (D) is the average speed, which is the distance traveled over time, of which distance traveled is half of the circumference. Response (B) is the radius over time.

Student responses
Sections 70854, 70855
(A) : 4 students
(B) : 13 students
(C) : 13 students
(D) : 15 students

"Difficulty level": 28%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.55