Physics quiz question: acceleration from velocity graph

Physics 205A Quiz 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of an object traveling in a straight line is shown at right. The object starts at x = 0 at t = 0. At t = 6 s, the acceleration is:
(A) −2 m/s².
(B) −1 m/s².
(C) 0 m/s².
(D) +1 m/s².
(E) +2 m/s².

Correct answer (highlight to unhide): (B)

The (instantaneous) acceleration at t = 6 s is the tangent slope of the v_x(t) graph at that instant in time. Since the slope of the v_x(t) graph is unchanged from t = 4 s to 9 s, then the average acceleration (given the chord slope) for that time interval will be identical to the instantaneous acceleration for any instant of time in that interval.

The average acceleration (which will be equal to the instantaneous acceleration) is then given by:

a_av,x = chord slope = ∆v_x/∆t = (−5 m/s)/(+5 s) = −1 m/s².

Sections 70854, 70855
Exam code: quiz02Bo74
(A) : 2 students
(B) : 38 students
(C) : 4 students
(D) : 2 students
(E) : 12 students

Success level: 66%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46