Halliday, Resnick & Walker — Kinetic Energy and Work: Problem 39

A force \(\vec{F} = (cx - 3.00x^2)\hat{i}\) acts on a particle as the particle moves along an \(x\) axis, with \(F\) in newtons, \(x\) in meters, and \(c\) a constant. At \(x = 0\), the particle’s kinetic energy is \(20.0\text{ J}\); at \(x = 3.00\text{ m}\), it is \(11.0\text{ J}\). Find \(c\).