Derive an expression for kinetic energy of an object

Asked by admin @ 11/08/2021 in Physics viewed by 301 People

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 @ 11/08/2021

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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