State and derive work energy theorem
Step 1. State work energy theorem
Work energy theorem states that the change in kinetic energy of an object is equal to the net work done on it by the net force.
Step 2. Derivation of work energy theorem
Let is the force applied on a body of mass to displace it a small distance along the direction of the force.
Then the work done by the force in displacing the object is
Also from Newtons second law of motion we get
Where is the force, mass and acceleration
From and we get
Now, work done by the force in order to increase its velocity from (initial velocity) to (final velocity) is given by
We know that K.E
is the rate of change of kinetic energy.
Therefore work done by a force is the rate of change of Kinetic energy