Question

derived mathematical derivation of knitic energy​

Answer 1

From equations of motion, the relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, s is But from Newton’s second law of motion F = m a. work done by the force, F is written as the following: If the object is starting from its stationary position, that is, u = 0, then From work and energy theorem, work done is equal to the change in the kinetic energy of the object. w = (1/2) mv 2 If u = 0, the work done will be, Thus the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is K.E = (1/2) mv 2

Answer 2

Hii..

we know that.

work done = F×S

now

by newton third law of motion

v^2-u^2=2at

as per eq 1-

We can write

F=ma

and in place of S we wrote newton third law of eq.

W=ma×v^2-u^2/2a

( both" a " are cancelled)

W= mv^2-mu^2/2

W=1/2m(v^2-u^2)

let , intial value be 0

So

we conclude that.

W=1/2m(v^2-0)

W=1/2mv^2

so in other words we can say that -

ke=1/2mv^2

Hence proved

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