Suppose that we'd like to move our destroyer on a straight line back and
forth between points 1000 meters from either side of the origin. Suppose that
the following equation gives our position (in meters) as a function of time:
where a is some constant. Small values for a will describe a faster
oscillation, and large values will describe a slower oscillation. By doing
graphical experiments using different values for a, what is the smallest
amount of time in which the destroyer can move from the origin, out to +1000
meters, back to -1000 meters, and then back to the origin without exceeding the
5 megawatt peak power capacity of the destroyer?