If a constant force `F` acts through a displacement `x` , it does work `W = Fx = (ma) x` on the particle.

Since the acceleration is constant, we can use the equation of kinematics .

Thus,

`W=(m[v_f^2-v_i^2])/2=1/2 mv_f^2-1/2 mv_i^2`.............(1)

The quantity, `x =1/2 mv^2` is a scalar and is called the kinetic energy of the particle. Kinetic energy is the energy that a particle posses by virtue of its motion . Thus, equation (1) takes the form

`Delta U=-Delta K`......................(2)

The work done by a force changes the kinetic energy of the particle . This is called the Work Energy Theorem.

In general, the net work done by the resultant of all the force acting on the particle is equal to the change in kinetic energy of a particle.

`W_(n et)=Delta k`..............(3)

And taking into account the work done by internal forces, we have

`W_(text(internal))+W_(external)=Delta k`


`text(Important :)`

1. The kinetic energy of an object is a measure of the amount of work needed to increase its speed from zero to a given value.

2. The kinetic energy of a particle is the work it can do on its surroundings in coming to rest.

3. Since the velocity and displacement of a particle depend on the frame of reference, the numerical values of the work and the kinetic energy also depend on the frame.