Physics quiz question: comparing displacements from velocity graph

Physics 205A Quiz 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of a car traveling along a straight line is shown at right. The object starts at x = 0 at t = 0. The car travels the greatest distance during the time interval(s):
(A) 0 ≤ t ≤ 3 s.
(B) 3 s ≤ t ≤ 5 s.
(C) 5 s ≤ t ≤ 7 s.
(D) 7 s ≤ t ≤ 8 s.
(E) (There is a tie.)
(F) (None of the above choices.)

Correct answer (highlight to unhide): (A)

The displacement of the car is the area bounded by the car's v_x(t) graph and the time axis. (Since the car is always traveling in the forward direction, then its distance traveled is the same as its displacement.)

The (green) area in the interval 0 ≤ t ≤ 3 s can be graphically counted as containing nine squares, corresponding to a distance traveled of 9 meters; while the (blue) area in the interval 5 s ≤ t ≤ 7 can be graphically counted as containing only eight squares, corresponding to a distance traveled of only 8 meters. (Similarly for each of the other time intervals.)

Thus the car traveled the greatest distance during the 0 ≤ t ≤ 3 s time interval, as this area is greater than compared to all the other time intervals.

Sections 70854, 70855, 73320
Exam code: quiz02SL1p
(A) : 30 students
(B) : 4 students
(C) : 14 students
(D) : 9 students
(E) : 1 student
(F) : 1 student

Success level: 51%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50