Halliday, Resnick & Walker — Kinetic Energy and Work: Problem 47

47 A machine carries a 4.0 kg package from an initial position of \(\vec{d}_i = (0.50 \text{ m})\hat{i} + (0.75 \text{ m})\hat{j} + (0.20 \text{ m})\hat{k}\) at \(t = 0\) to a final position of \(\vec{d}_f = (7.50 \text{ m})\hat{i} + (12.0 \text{ m})\hat{j} + (7.20 \text{ m})\hat{k}\) at \(t = 12 \text{ s}\). The constant force applied by the machine on the package is \(\vec{F} = (2.00 \text{ N})\hat{i} + (4.00 \text{ N})\hat{j} + (6.00 \text{ N})\hat{k}\). For that displacement, find (a) the work done on the package by the machine’s force and (b) the average power of the machine’s force on the package.