Physics quiz question: average speed versus average velocity

Physics 5A Quiz 3, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 3.26

[Version 1]

[3.0 points.] A car travels west at 80 km/h for 1.0 h. It then travels north at 45 km/h for 1.0 h. Which quantity has a larger magnitude for the car during this trip?
(A) The average speed.
(B) The average velocity.
(C) (Both average speed and average velocity have the same magnitude.)
(D) (Not enough information is given to determine this.)

Correct answer: (A)
The average speed is the distance traveled divided by the elapsed time, which is (80 km + 45 km)/2.0 h = 63 km/h. The average velocity is the displacement (straight-line distance from start to finish) divided by the elapsed time, which is sqrt((80 km)^2 + (45 km)^2)/2.0 h = 46 km/h.

Student responses
Sections 0906, 0907
(A) : 5 students
(B) : 10 students
(C) : 6 students
(D) : 0 students

[Version 2]

[3.0 points.] A car travels west at 80 km/h for 1.0 h. It then travels north at 45 km/h for 1.0 h. Which quantity has a smaller magnitude for the car during this trip?
(A) The average speed.
(B) The average velocity.
(C) (Both average speed and average velocity have the same magnitude.)
(D) (Not enough information is given to determine this.)

Correct answer: (B)

Student responses
Sections 0906, 0907
(A) : 7 students
(B) : 6 students
(C) : 7 students
(D) : 0 students