Derive an expression for kinetic energy of a body


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Derive an expression for kinetic energy possessed by an object of mass m moving with velocity v. also state si unit of kinetic energy.

Answered by admin @



Consider a body of mass "m" moving with an initial velocity "u".
A constant force "F" acts on it and the velocity changes to "v".

Let "s" be the distance covered and "a" be the constant acceleration


We know that

v² - u² = 2as

s =  \frac{v^{2}  - u ^{2} }{2a}


We know that ,

Work done = Force(F) × displacement (s)

F = ma


W = ma × \frac{v^{2}  - u ^{2} }{2a}


["a" gets cancelled ]

W = m × \frac{v^{2}  - u ^{2} }{2}
=  \frac{1 }{2} m[v² - u² ]


When , initial velocity , u = 0

W =  \frac{1 }{2} mv²

K.E = Work done
=  \frac{1 }{2} mv²

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