An auto accident, a car hit a pedestrian and the driver then slammed on the brak

Question

An auto accident, a car hit a pedestrian and the driver then slammed on the brakes to stop the car.  During the subsequent trial, the driver's lawyer's claimed the he was obeying the posted 35 mi/h speed limit, but that the legal speed was too high to allow him to see and react to the pedestrian in time.  You have been called in as the state's expert witness.  Your investigation of the accident found that the skid marks made while the brakes was applied were 280ft long, and the tread on the the tires produced a coefficient of kinetic friction of .30 with the road.  a) in your testimony in court, will you say that the driver was obeying the post speed?   You must be able to back up your conclusion with clear reasoning because one of the lawyers will surely cross-exam you. b) if the driver speeding ticket were $10 for each mile per hour he was driving above the posted speed limit, would he have topay a fine> If so, how much would it be?

Explanation / Answer

the idea is that the skid marks represent the distance the carslid to a stop. This was due to friction, so... .      acceleration = force offriction / mass = m g / m = g . Also       v2 = 2 a d   = 2 gd = 2 * 0.30 * 32 ft/s2 * 280 ft = 5376 ft2 / s2 . So his speed was    v =   73.32feet per second =     50.0miles per hour . So no, the driver was not obeying the speed limit. And hewould have to pay $10 * (50 - 35) = $150 fine . So his speed was    v =   73.32feet per second =     50.0miles per hour . So no, the driver was not obeying the speed limit. And hewould have to pay $10 * (50 - 35) = $150 fine .      

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