The perfect speed bump

This article presents a thought experiment where the reader, as a highways technician, must shape a speed bump from a fixed volume of concrete to minimize discomfort. Using physics principles like conservation of energy and calculus, the author derives equations for velocity and vertical acceleration as a function of the bump's shape. The goal is to minimize the integral of squared vertical acceleration over the bump, leading to a complex optimization problem involving differential equations. The article explores the mathematical approach to finding the optimal curve y(x) that reduces the jolt experienced by a car.