Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_90

3/90 The position vector of a particle is given by \(\mathbf{r} = 8t\mathbf{i} + 1.2t^2\mathbf{j} - 0.5(t^3 - 1)\mathbf{k}\), where \(t\) is the time in seconds from the start of the motion and where \(\mathbf{r}\) is expressed in meters. For the condition when \(t = 4 \text{ s}\), determine the power \(P\) developed by the force \(\mathbf{F} = 40\mathbf{i} - 20\mathbf{j} - 36\mathbf{k} \text{ N}\) which acts on the particle.