Physics quiz question: comparing average accelerations from velocity graph

Physics 205A Quiz 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

The v_x(t) graph of two cars traveling in a straight line are shown at right. The object starts at x = 0 at t = 0.

_________ experiences the greater magnitude average acceleration from t = 0 to t = 8 s.
(A) Car 1.
(B) Car 2.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

For car 1, since the slope of its v_x(t) graph is unchanged from t = 0 to t = 8 s, then the average acceleration (given by the chord slope) for that time interval will be identical to the tangent slope for any instant of time in that interval, given by:

car 1: a_av,x = chord slope = (+6 m/s)/(8 s) +0.75 m/s².

For car 2, since the slope of its v_x(t) graph changes at t = 4 s, then the average acceleration must be explicitly given by the chord slope that has endpoints at t = 0 and t = 8 s:

car 2: a_av,x = chord slope = ∆v_x/∆t = (3 m/s)/(+8 s) = +0.375 m/s².

Sections 70854, 70855, 73320
Exam code: quiz02J3eP
(A) : 42 students
(B) : 13 students
(C) : 16 students
(D) : 0 students

Success level: 57%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.69