of work is said to be path dependent. The time derivative of the integral for work yields the instantaneous power, If the work for an applied force is independent of the path, then the work done by the force is, by the gradient theorem , the potential function evaluated at the start and end of the trajectory of the point of application. Such a force is said to be conservative . This means that there is a potential function U ( x ), that can be evaluated at the two points x (t 1 ) and x (t 2 ) to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is The function U ( x ) is called the potential energy associated with the applied force. Examples of forces that have potential energies are gravity and spring forces. Because the potential U defines a force F at every point x in space, the set of forces is called a force field . The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity V of the body, that is Gravity exerts a constant downward force on every object. Near the surface of the earth the acceleration due to gravity is g=9.8 m.s −2 and the gravitational force on an object of