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

11 A 3.0 kg object is driven along an x axis by a variable force that is directed along that axis. Its position is given by $x = 4.0\text{ m} + (5.0\text{ m/s})t + kt^2 - (3.0\text{ m/s}^3)t^3$, where $x$ is measured in meters and $t$ in seconds. The factor $k$ is a constant. At $t = 4.0\text{ s}$, the force on the particle has a magnitude of 37 N and is in the negative direction of the axis. Find the value of $k$.