A motorcycle is coasting along at a constant velocity of 20.0 m/s. The motorcyclist suddenly hits a rough patch in the road where the coefficient of kinetic friction is 0.800. Can the motorcycle clear the rough patch on the road without re-starting the engine if the patch is 15.0 m long? If so, what will be the cyclist‘s velocity upon leaving the rough patch?
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A motorcycle coasting on a road doesn't care about the coefficient of kinetic friction. We only use the coefficient of kinetic friction in sliding scenarios, whereas the motorcycle is rolling (on wheels). Since the motorcycle is going at a constant velocity (not speeding up or turning), the only time it would encounter sliding motion is if it hit a slick patch, not a rough patch. That being said, going at 20 m/s over a 15 m patch takes less than a second. As long as he keeps his balance and doesn't lean or turn accelerate or brake he should be okay. He should probably lay off the gas though.
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