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## by Chatham Napoli

Submitted : Spring 2016

Many individuals cringe at the sight of red and blue lights in the rear view, feeling a sudden emptiness when coming to the realization that a costly speeding ticket was in the near future. However, this was not the case in this situation. A ticket from the Florida Highway Patrol was received in the mail with no recollection of being pulled over, it was evident through preliminary research that a form of calculus was used in determining the vehicle ’s speed. Since speeding tickets are expensive and normally start well over one hundred dollars, it deems an appropriate topic of study. The idea is that an accurate method must used in calculating the miles per hour a vehicle is traveling without the standard radar detecting device. The routine used by the police force for the described scenario is called the Mean Value Theorem. In simpler terms, the Mean Value Theorem is applied to find values for the derivative that exists. This is because the theorem states that at least one point in between two points must be equivalent to the slope of the tangent line and the slope of the secant line in between the same two points. This research will provide information regarding the calculus applied to traffic violations, as well as address why this particular process of ticketing is proven to be justified.

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 Advisors : Arcadii Grinshpan, Mathematics and Statistics Anthony Napoli, Florida Highway Patrol Suggested By : Nathaniel Whitney