The coefficient of friction between a racecar's wheels and the track is 1.0.The car starts from rest and accelerates at a constant rate for 275 m.Find the maximum speed at the end of the race.
A)52 m/s
B)57 m/s
C)73 m/s
D)86 m/s
E)66 m/s

Question

Quizplus · Accepted Answer

First, find the maximum acceleration the car can have:

μ = F_friction/F_normal

F_friction = μF_normal

F_normal = mg

F_friction = μmg

a_max = F_friction/m

a_max = μg

a_max = 1.0 × 9.81 m/s^2

a_max = 9.81 m/s^2

Then, use the kinematic equation:

v_f^2 = v_i^2 + 2ad

v_i = 0 m/s (starting from rest)

d = 275 m

v_f^2 = 2a_maxd

v_f^2 = 2 × 9.81 m/s^2 × 275 m

v_f^2 = 5394.75 m^2/s^2

v_f = 73.4 m/s

Rounding to the nearest whole number gives:

v_f = 73 m/s

Therefore, the answer is choice C.

The Coefficient of Friction Between a Racecar's Wheels and the Track