Question

derive the relationship KE=1/2mv2 where M is the mass and V is the velocity of the body

Answer 1

Kinetic Energy:-

The kinetic energy of a moving body is measured by the amount of work it can do before coming to rest.

Consider a body of mass 'm' moving with an initial velocity 'u'. When a force 'F' is applied on it , which displaces the object through a distance 's' and it's final velocity changes to 'v' and it produces an acceleration 'a'.

We know that,

v^2 - u^2 = 2as
s = v^2 - u^2/2a

Work done(W) = F × s

We know from Newton's second law of motion F = ma

W = ma × (v^2 - u^2/2a) (or)

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

When the object starts from rest then it's initial velocity u = 0

Hence,

W = 1/2mv^2

This work done is stored in a form of KE

Therefore,

KE = 1/2 mv^2

Hope my answer helps you :)

Regards,
Shobana