A Simple Destroyer Model

Let's begin by assuming that we know the position of the destroyer as a function of time, and that we want to calculate the power required to move the destroyer along this path. Once we know how to solve this problem, we will be able to generalize our approach to determine the power required to move the destroyer along an arbitrary path.

Given a position function, we can obtain velocity and acceleration functions by differentiation. Once we know the acceleration of the destroyer, we can easily calculate the force required to produce that acceleration via Newton's familiar F = ma. Let's assume that the mass of the destroyer is 5000 tons, or 4.5e6 kilograms. Finally, once we know the required force, we can compute the power requirements by multiplying force and velocity.

To keep things simple for now, let's assume that the destroyer is moving in a straight line. And to keep things concrete, let's assume that the destroyer's position at time t, expressed in meters, is:

position := t -> .01*t^2 + t;