# What is kinetic energy? Derive an equation for the kinetic energy of a body of mass ‘m’ moving at a speed ‘v’.

A body in motion posses kinetic energy

Let us assume that an object of mass(m) is at rest on a smooth horizontal plane as shown above . Let it be displaced through a distance ‘s’ from the point A to B by force(F) acting upon it in the direction of the displacement. In the horizontal direction the net force is equal to the applied force F.

The work done on the object by the net force W = Fxs ---(i)

Let the work done on the object cause a change in its velocity from ‘u’ to ‘v’ and the acceleration produced be ‘a’

The relation between initial velocity u, final velocity v, acceleration ‘a’ and displacement ‘s’ is given from the equation of motion as

---(ii)

By newton’s second law of motion

F = m x a --(iii)

From equation (i), (ii) (iii) ,we have

Note:- A Special case is when the object is initially at rest i.e u = 0 ,In that particular case ,Formula of Kinetic Energy comes to be K.E = .

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