Work Energy Theorem

Derivation

Let a body is initially at rest and force F is applied on the body to displace it through ds along its own direction then small work done .

[As F = ma]

Therefore work done on the body in order to increase its velocity from zero to v is given by

This work done appears as the change in  kinetic energy of the body

In vector form

Work done = change in kinetic energy

 

This is work energy theorem, it states that work done by a force acting on a body is equal to the change produced in the kinetic energy of the body.

This theorem is valid for a system in presence of all types of forces (external or internal, conservative or non-conservative).

If kinetic energy of the body increases, work is positive i.e. body moves in the direction of the force (or field) and if kinetic energy decreases work will be negative and object will move opposite to the force (or field).