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Derive the formula for the kinetic energy of an object of mass m, moving with velocity v.

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Suppose a stationary object of mass ‘m’ moves because of an applied force. Let ‘u’ be its initial velocity (here u = 0). Let the applied force be ‘F’. This generates an acceleration a in the object, and after time T, the velocity of the object becomes equal to ‘v’. The displacement during this time is s. The work done on the object is

W = F x s ……………….. (1) 

Using Newton’s 2nd law of motion, 

F = ma ……………….. (2) 

Using Newton’s 2nd equation of motion

\(s = ut+\cfrac{1}{2}at^2\)

However, as initial velocity is zero, u = 0

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