Every day, I see someone say that math is pointless and that it cannot be used outside of the classroom. But math is a special subject that can describe incredible phenomena or predict simpler things, like who will win the Super Bowl. One of the most interesting applications of mathematics I found while researching was using the mean value theorem to issue speeding tickets.
The mean value theorem uses calculus to introduce an important concept to us. The mean value theorem states that if "f" is a differentiable equation and in the set a-b there is a value c within the set, then f'(c) =f(b)-f(a)b-a . Now to all of the readers who have not taken calculus yet, this equation may look like a bunch of letters scrambled around in a nonsensical order. In simpler terms, the theorem just states that at some time in the interval a-b you were traveling at the average speed.
For example, if I wanted to go from my house, point A, to the supermarket, point B, which is 5 miles away, we can use the theorem. If I traveled to the supermarket in a total of 5 minutes, this means at a certain point in my journey I was traveling at 1 mile per minute or 60 miles per hour. If the speed limit of the road leading to the supermarket is 45 miles, then I can be issued a speeding ticket because I was traveling 60 miles at a certain instant. This can also be explained using physics by using position and velocity equations. Since velocity is the first derivative of position, the theorem states that at a certain point C my velocity is equivalent to the average speed traveled from a-b.
In theory, this theorem makes sense, but we have to raise the question “Is this viable in the real world?” I say that for the majority of instances, this method is viable. By implementing cameras with advanced cameras and technology, you can very easily determine the time it takes for a car to travel a certain distance. Using a little bit of calculus from there can tell law enforcement officers whether or not you were speeding. Assuming that we have a certain range of errors with our cameras, a computer program can very easily determine if a ticket should be issued or not. This simple solution can greatly reduce the number of officers we need patrolling the highways and allows us to be more eco-friendly.
A system similar to the proposed one has been implemented in Scotland for research purposes. Cathay Jameison, Justice Minister of Scotland and spokesperson of this project, states that the aim of the project was to not catch speeding motorists but rather to promote safer driving in the area. All in all, we see math truly is everywhere around us and the possibilities of integrating math into the real world are endless.
Sources
Richeson, Dave. “E-Z Pass, Speeding Tickets, and the Mean Value Theorem.” David Richeson: Division by Zero, 23 Oct. 2008, divisbyzero.com/2008/10/22/e-z-pass-speeding-tickets-and-the-mean-value-theorem/.
“Specs Spies on Speeding Motorists.” News.bbc.co.uk, 14 July 2005, news.bbc.co.uk/2/hi/uk_news/scotland/4681507.stm. Accessed 7 Mar. 2021.