Question

Prove that the kinetic energy of a body of mass m moving with velocity v is given by: Ek = 1/2 mv2​

Answer 1

Explanation:

Let that

the body moves with the acceleration A

the body moves with the acceleration Aand the initial point be U and

the body moves with the acceleration Aand the initial point be U and reaches to final Velocity V

the body moves with the acceleration Aand the initial point be U and reaches to final Velocity Vand covered the distance S

Apply 3rd equation of motion

v² = u²+ 2as

v² - u² = 2as

$\frac{ {v}^{2} - {u}^{2} }{2a} = s \\ so \: it \: means \\ \frac{ {v}^{2} - {u}^{2} }{2a} ..(1)$

Now we know that work done is

Work done =

$force \times displacement$

and force =

$mass \times acceleration$

therefore

$w = m \times a \times s$

let's put the value of S means equation (1) in equation

$w = m \times a \times \frac{ {v}^{2} - {u}^{2} }{2a } \\ w = m \times ( {v}^{2} - {u}^{2} )$

now we know that intial point will be 0 therefore putting the value of u as 0(zero)

$w = \frac{m {v}^{2} }{2}$

therefore

Ek =

$\frac{1}{2} \times m {v}^{2}$