Physics quiz question: position from velocity graph

Physics 205A Quiz 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 2.11

Consider this v_x(t) graph of an object traveling in a straight line. The object starts at x = 0 at t = 0. At t = 6 s, the object is located at:
(A) –6 m.
(B) –2 m.
(C) 0 m.
(D) +2 m.
(E) +6 m.

Correct answer: (E)

The displacement delta(x) is given by the area bounded by the v_x(t) graph from t = 0 to t = 6 s, which is a triangular area:

delta(x) = (1/2)*base*height = (1/2)*(2 m/s)*(6 s) = +6 m,

which is positive because velocity was positive during this time interval (the bounded area is above the time axis). Since the object started at x = 0 at t = 0, then at t = 6 s, the object is located at x = +6 m.

Sections 70854, 70855
Exam code: quiz02p4iN
(A) : 3 students
(B) : 3 students
(C) : 27 students
(D) : 3 students
(E) : 17 students

Success level: 32%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72