Work and Kinetic Energy

The capacity to do work is called energy. If a system (object) has energy, it has ability to do work. An automobile moving on a road uses chemical energy of fuel (CNG, petrol, diesel). It can push an object which comes on its way to some distance. Thus it can do work.

All moving objects possess energy because they can do work before they come to rest. This kind of energy is called as kinetic energy. Kinetic energy is the energy of an object because of its motion.

Consider an object of mass m moving along a straight line when a constant force of magnitude F acts on it along the direction of motion. This force produces a uniform acceleration a such that F = ma. Let v₁ be the speed of the object at time t₁. This speed becomes v₂ at another instant of time t₂. During this interval of time t = (t2 – t1), the object covers a distance s. Using Equations of Motion,

v₂² = v₁² + 2as

a = (v₂² – v₁²)/2s

Combining this result with Newton’s second law of motion,

F = m × (v₂² – v₁²)/2s

Work done by the force is given by

W = Fs

W = m × (v₂² – v₁²)/2

W = ½mv₂² – ½mv₁²

W = K₂ – K₁

where K₂ and K₁ respectively denote the final and initial kinetic energies. (K₂ – K₁) denotes the change in kinetic energy, which is equal to the work done by the force.

Kinetic Energy is a scalar quantity. It depends on the product of mass and the square of the speed. It does not matter which one of the two (m and v) is small and which one is large. 

K = ½mv²

Work-Energy Theorem

The work-energy theorem states that the work done by the resultant of all forces acting on a body is equal to the change in kinetic energy of the body.