Walker, Halliday & Resnick — Kinetic Energy and Work: Problem 31

31 As a 2.5 kg body moves in the positive direction along an x axis, a single force acts on it. The force is given by \(F_x = -6x \text{ N}\), with \(x\) in meters. The velocity at \(x = 3.5 \text{ m}\) is \(8.5 \text{ m/s}\). (a) Find the velocity of the body at \(x = 4.5 \text{ m}\). (b) Find the positive value of \(x\) at which the body has a velocity of \(5.5 \text{ m/s}\).