Halliday, Resnick & Walker — Force and Motion–I: Problem 11

A 2.0 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by \(x = 3.0 \text{ m} + (4.0 \text{ m/s})t + ct^2 - (2.0 \text{ m/s}^3)t^3\), with \(x\) in meters and \(t\) in seconds. The factor \(c\) is a constant. At \(t = 3.0 \text{ s}\), the force on the particle has a magnitude of 36 N and is in the negative direction of the axis. What is \(c\)?