Force of Friction
Power (P)
Power is defined as the work done per second (or, power is the rate of doing work).
Thus, Power 
(where v = velocity)
The S.I. unit of power is J/second or watt (W). The watt is defined as the rate of working at 1 Joule per second.
1kW = 1000W
1MW = 106 W
1 Horse power = 746 W
Work can also be expressed in units of power × time. This is the origin of the term kilowatt × hour, For example, one kilowatt hour is the work done in 1 hour by an agent working at the rate of 1 kilo-watt.
Positive and Negative Work
If q between 
and 
is an acute angle then the work done by the force is positive. Positive work means that the force (or its component) is along the direction of displacement. On the other hand work done is negative if q is an obtuse angle. Negative work means that force (or its component) is opposite to the displacement.
As an illustration, when a person goes upstairs he is doing positive work against the force of gravity but the work done by the force of gravity on that person is negative.
Again when a body is pulled on a rough level surface, the work done by the pulling force is positive but the work done by frictional force is negative.
An interesting result: If value of q between and 
be exactly equal to 90º, then inspite of the fact that a force is being applied and displacement is also taking place, the work done is zero. Work done by a coolie while carrying a load on a railway platform against gravity is zero. Again for uniform circular motion work done by centripetal force is zero because displacement is at right angle to the direction of force. Similarly work done by Lorentz magnetic force on a moving charged particle, work done by a coulombian force on electron revolving in its orbit, work done by gravitational force on motion of planets and satellites is also zero.
Work Done By a Variable Force
When the force is an arbitrary function of position, we need the techniques of calculus to evaluate the
work done by it. The figure shows
as some function of the position x. We begin by replacing the actual variation of the force by a series of small steps. The area under each segment of the curve is approximately equal to the area of a rectangle. The height of the rectangle is a constant value of force, and its width is a small displacement Dx. Thus, the nth step involves an amount of work DWn=Fn Dxn. The total work done is given approximately by the sum of the areas of the rectangles : 
As the size of the steps is reduced, the tops of the rectangles more closely trace the actual curve shown in fig. In the limit 
which is equivalent to letting the numbers of steps tend to infinity, the discrete sum is replaced by a continuous integral.
Thus, the work done by a force, Fx from an initial point A to final point B is
Work depends on the frame of reference: With change of frame of reference (assuming it to be an inertial frame) force does not change. However, the displacement changes. Consequently work done will be different in different frames.
Example 1: Consider a man pushing a box inside a moving train. In the frame of train the work done is 
where
is displacement of box with respect to its initial position in train. However, in the frame of earth the work done is 
where s0 is the displacement of the train relative to ground during that time.
Example 2: Consider a porter with luggage on his head moving up a staircase. Work done by the lifting force relative to porter is zero but relative to ground work done is finite and positive.
Conservative and non-conservative forces
Conservative forces are the forces, work done by which are independent of the path followed. The amount of work simply depends on initial position and final position but is independent of the actual path followed. Moreover, work done by a conservative force for a closed path, where final position is same as the initial position, is always zero. Gravitational force, force of gravity, electrostatic force are examples of conservative forces.
Non-conservative forces are those for which work done depends on the actual path followed. Force of friction, viscous force due to fluids etc. are examples of non-conservative forces.