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Notions of Work and Kinetic Energy: The Work-Energy Theorem

The relation for rectilinear motion under constant acceleration is a
v2 - u2 = 2as

where u and v are the initial and final speeds and s the distance traversed. Multiplying both sides by m/2, we have
mv2 - mu2 = mas = Fs

where the last step follows from Newton's Second Law. We can generalise to three dimensions by employing vectors
v2 - u2 = 2 a. d

Once again multiplying both sides by m/2, we obtain
mv2 - mu2 = m a. d = F. d

This equation provides a motivation for the definitions of work and kinetic energy. The left side of the equation denotes difference in the quantity "half the mass times the square of the speed" from its initial value to its final value. 

We call each of these quantities the 'kinetic energy', denoted by K. The right side is a product of the displacement and the component of the force along the displacement. This quantity is called 'work' and is denoted by W. 
Kf - Ki = W

Where Ki and Kf are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts. Work is done by a force on the body over a certain displacement.

The change in kinetic energy of a particle is equal to the work done on it by the net force.

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