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Before 1960, people believed that the maximum attainable coefficient of static friction for an automobile tire on a roadway was μs = 1. around 1962, three companies independently developed racing tires with coefficients of 1.6. this problem shows that tires have improved further since then. the shortest time interval in which a piston-engine car initially at rest has covered a distance of one-quarter mile is about 4.43 s. ]

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shinmin

This problem is looking for the minimum value of μs that is necessary to achieve the record time. To solve this problem:


Assuming the front wheels are off the ground for the entire ¼ mile = 402.3 m, the acceleration a = µs·9.8 m/s².


For a constant acceleration, distance = 402.3


m = 1/2at^2 = 804.6 m / (4.43 s)^2 = a = µs·9.8 m/s^2



µs = 804.6 m / (4.43s)^2 / 9.8 m/s^2 = 4.18