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Work Energy Theorem

The work-energy theorem also known as the principle of work and kinetic energy
states that the total work done by the sum of all the forces acting on a particle is
equal to the change in the kinetic energy of that particle.

Derivation
The work ‘W’ done by the net force on a particle is equal the change in the particle’s
kinetic energy (KE).

Check the detailed work-energy theorem derivation given below.

Let us consider a case where the resultant force ‘F’ is constant in both direction and
magnitude and is parallel to the velocity of the particle. The particle is moving with
constant acceleration along a straight line. The relationship between the acceleration
and the net force is given by the equation “F = ma” (Newton’s second law of motion),
and the particle’s displacement‘d’, can be determined from the equation:

Obtaining,

The work of the net force is calculated as the product of its magnitude (F=ma) and
the particle’s displacement. Substituting the above equations yields:

Relation between Momentum and Kinetic Energy
Kinetic energy and momentum of a moving body can be mathematically related as
follow-

Consider the formula of kinetic energy-