|Work done by a variable force: two –dimensional case:|
In two dimensions the force is having two components along x and y directions respectively. Then the work done by the variable force in two dimensions can be given as:
Thus, the mathematical representation of work-energy theorem can be given by,
where vi and vf are the initial and final velocities of the particle. In a more convenient manner the net work done can be written as:
It can be noted that the work energy theorem is valid for both constant as well as variable force.