Halliday, Resnick & Walker — Kinetic Energy and Work: Problem 50

(a) At a certain instant, a particle-like object is acted on by a force \(\vec{F} = (4.0 \text{ N})\hat{i} - (2.0 \text{ N})\hat{j} + (9.0 \text{ N})\hat{k}\) while the object's velocity is \(\vec{v} = -(2.0 \text{ m/s})\hat{i} + (4.0 \text{ m/s})\hat{k}\). What is the instantaneous rate at which the force does work on the object? (b) At some other time, the velocity consists of only a \(y\) component. If the force is unchanged and the instantaneous power is \(-12 \text{ W}\), what is the velocity of the object?