When the applied force is not constant, the equation W = f x D, which calculates work, becomes invalid. This equation only applies when both force and distance are constant and measured in the same direction. To analyze variable forces, a more general approach involving calculus and vectors is necessary. By considering small increments of distance and summing the contributions of force over the total distance, one can calculate work done under varying forces. Understanding these concepts is essential for accurately determining work in dynamic systems.