Question

derive expression for 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. It is clear that the work done is equal to the change in the kinetic energy of an object. If u = 0, the work done will be 2 m v 2 .

Answer 2

we know that

v²-u²=2as

s=v²-u² upon 2a

work done =force x displacment

f=ma

w=ma x v²-u² upon 2a

(a gets cancelled)

w=m x v²- u² upon 2

half m(v²-u²)

when initial velocity u=0

w= half mv²

ke=work done

=half mv²