Physics quiz question: Kia Telluride braking time

Physics 205A Quiz 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

"2020 Kia Telluride"
Automotive Rhythms

According to Car and Driver magazine[*] a 2020 Kia Telluride SX AWD sports utility vehicle was able to slow down from an initial speed of 31 m/s to a complete stop over a distance of 49 m. Assume that the road is horizontal, and that the acceleration of the Kia Telluride is constant and always points in the opposite direction from its velocity. While the Kia Telluride slowed down to a complete stop, the elapsed time was:
(A) 0.057 s.
(B) 0.32 s.
(C) 1.8 s.
(D) 3.2 s.

[*] David Beard, "The 2020 Kia Telluride Is Set to Win Big in the Three-Row SUV Segment," caranddriver.com/reviews/a26965174/2020-kia-telluride-drive/.

The following quantities are given (or assumed to be known):

(t0 = 0 m),
(x0 = 0 m),
x = +49 m,
v0x = +31 m/s,
vx = 0 m/s.

So in the equations for constant (average) acceleration motion in the horizontal direction, the following quantities are unknown, or are to be explicitly solved for:

vx = v0x + ax·t,

x = (1/2)·(vx + v0xt,

x = v0x·t + (1/2)·ax·(t)2,

vx2 = v0x2 + 2·ax·x.

With the unknown quantity t to be solved for appearing in the second equation, with all other quantities given (or assumed to be known), then:

x = (1/2)·(vx + v0xt,

t = 2·x/(vxv0x) = 2·(+49 m)/(+31 m/s − 0 m/s) = 3.1612903226 s,

or to two significant figures, t = 3.2 s.

(Response (A) is sqrt(vx)/(2·x); response (B) is vx/(2·x); response (C) is sqrt(vx/(9.80 m/s2)).)

Sections 70854, 70855
Exam code: quiz02Cs1o
(A) : 2 students
(B) : 4 students
(C) : 4 students
(D) : 44 students

Success level: 81%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46

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