According to this theorem, the work done by a force on a particle is same to the change in the kinetic energy of the particle.

We know that the quantity F × dS = F dS cosΘ is described as the work done by force F on the particle during small displacement dS. When the force F performs on the particle during a finite displacement, the work done is calculated as,

                                                                           ....(i)

Suppose that a object of mass m is performed upon by a resultant acceleration force F along the X-axis. Consider the body moves from a position x₁ to position x₂ along X-axis. Let the speed of the object increases from v₁ and v₂. The work done by the force in the displacement is

                                                                                                       ...(ii)

But according to Newton's second law, 

Substituting this value in eq. (2), we get

                                       ... (iii)

where the quantity  is called 1/2mv²as the kinetic energy of the object. K_f and K_i are the initial and final kinetic energies of the body.

If  ΔK be the change in kinetic energies, then

 Note: - Work-energy theorem is particularly useful in detemination of minimum stopping force or minimum stopping distance. If a object is brought to a halt, the work done to do so is same to the kinetic energy lost.

Mechanical energy:

Mechanical energy E of particle, system or object is described as the sum of kinetic energy K and potential energy U, i.e. E = K + U. It is a scalar quantity having dimensions [ML²T^-2] and SI unit joule.

(i) It relays on frame of reference.

(ii) A body may have mechanical energy without having either kinetic energy or potential energy. However, if both potential and kinetic energies are zero, mechanical energy will be zero. The result may or may not be true, i.e., if E = 0 either both KE and PE are zero or PE negative and KE positive such that KE + PE = 0.

Examples: Law of conservation of mechanical power

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