in the equation w= fd it is assumed that the force varies and is exerted in the direction of displacement... true or false?

Yes. Force is measured in the direction of displacement.

False. In the equation w = fd, the assumption is that the force is constant and is exerted in the direction of displacement. The equation represents the work done (w) on an object by a force (f) that acts in the same direction as the displacement (d) of the object. Work is the product of the force and the displacement, but it only holds if the force remains constant and acts in the same direction as the displacement.