Your car tire is rotating at 3.6 rev/s when suddenly you press down hard on the

Question

Your car tire is rotating at 3.6 rev/s when suddenly you press down hard on the accelerator. After traveling 192 m, the tire's rotation has increased to 6.2 rev/s. If you were initially driving at 16 mph: a) what is the radius of your car tire, in m? Use 1 mile = 1609 m. b) Through what angle, in radians, has the tire turned in the 192 m? c) What was the tire's angular acceleration, in rad/s/s? d) How long, in seconds, did the acceleration take? Help with any of these would be greatly appreciated. Thanks

Explanation / Answer

16 mph = 7.15 m/s
a) v = w r
7.15 = (3.6*2*pi)*r
r=0.316 m
b) theta = distance/r = 192/0.316=607.6
c)
w^2 = w0^2 + 2 alpha theta
(6.2*2*pi)^2 = (3.6*2*pi)^2 + 2*alpha*607.6
alpha=0.828

d) w = w0 + alpha t
(6.2*2*pi) = (3.6*2*pi) + 0.828*t
t=19.73 s

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