Question

Derive an expression for kinetic energy of a moving object of a mass m moving with a uniform velocity v

Answer 1

let, the body of mass m move with a certain initial velocity u and final velocity v

lets now consider the initial velocity as 0

we know that force = mass x acceleration or m*a

we also know that relating all the velocity and acceleration formula is v2 - u2=2as

or rewritten as s  =  v2-u2/2a

thus apply these in W = f x s

or we get W =m x a x v2-u2 / 2a {because s = displacement}

when we take u = 0 then u gets cancelled and strike out the a's we get w = 1/2 mv2

the kinetic energy k=1/2 mv2