Work
Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of force.
Let a constant force 
be applied on the body such that it makes an angle θ with the horizontal and body is displaced through a distance s
be applied on the body such that it makes an angle θ with the horizontal and body is displaced through a distance s
By resolving force
into two components :
(i) F cos θ in the direction of displacement of the body.
(ii) F sin θ in the perpendicular direction of displacement of the body.
Since body is being displaced in the direction of 
, therefore work done by the force in displacing the body through a distance s is given by
, therefore work done by the force in displacing the body through a distance s is given by
or 
Thus work done by a force is equal to the scalar or dot product of the force and the displacement of the body.
If a number of force 
are acting on a body and it shifts from position vector 
to position vector 
then 
.
are acting on a body and it shifts from position vector to position vector then .Unit of Work
Since work is the product of force and distance, unit of work is unit of force and unit of distance. If force is in N and distance is in metres, unit of work will be N-m. In SI system of unit, 1N-m = 1 J. The term Joule s used for one N-m work done, and letter J is used as a symbol of Joule. Hence, one Joule may be defined as the amount of work done by one Newton force when it moves one metre distance in its direction.
Energy
The energy of a body is defined as its capacity for doing work. Since energy of a body is the total quantity of work done therefore it is a scalar quantity.
Power
Power of a body is defined as the rate at which the body can do the work.
Average power 
Instantaneous power 
[As 
]
[As ]
[As 
]
i.e. power is equal to the scalar product of force with velocity.
If work done by the two bodies is same then power
i.e. the body which perform the given work in lesser time possess more power and vice-versa. As power = work/time, any unit of power multiplied by a unit of time gives unit of work (or energy) and not power.
Work Done by Variable Force
Let a varying force P move a body by distance s as shown by force-displacement curve in Fig.. At an instance, when force P is acting and the body moves by an elemental distance ' δs', then work done at that instance
= P δ s
Hence work done by the varying force in moving the body by distance ‘s’
= Σ P δ s
and it is equal to the area under the force-displacement curve. The variation of force is in a regular fashion so that its value at any instance can be represented by an expression. Then the work done can be evaluated by suitable integration. In such a case,
work done= ΣPs = ∫ Pds
