Question

Drive an expression of kinetic energy

Answer 1

Expression for kinetic energy :

Suppose a Force ‘F’ acting on a body of mass ‘m’ in state of rest changes its velocity to ‘v’ and body covers ‘s’ distance in the direction of force.

Then, the work done by the force is given by

W = F . S

= ma . S …………(1) [ F = ma ]

Now, using equation of motion, we have

v2 = u2 + 2aS

or, v2 = 0 + 2aS

as = v2/2

So, by equation (1) , we get

W = m .v2/2

so , by definition of kinetic energy of the body,

K.E. = W = 1/2 mv2

Answer 2

Explanation:

Hey dear✋☺

⌲Let a body of mass m is initially at rest is acted upon by a constant force F

Let it acquires final velocity v after displacement S

then,

v² - u² = 2as

v² - 0 = 2as ( u = 0)

a = v²/2s

but F = ma

F = m.v²/2s

and W = F.S

W = mv²/2S x S

⌲w = ½mv²