Question

Derive the expression for work-energy of a body in motion.

Answer 1

The Work-Energy Theorem. The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.

Answer 2

let the body of mass 'm' is moving with a velocity 'v'. A force F is applied on it to stop its motion for which the retardation 'h' is produce in the body and the body covers a distance's' before coming in rest

work done by the force to stop the motion of the body is the measure of kinetic energy -

Here

initial velocity = v
final velocity = o( zero )

from newton's 2nd law
F=ma
or a = f/m

from newton's 3rd law
0 = v^2-2as
or, 2as-v^2
or, 2*F/m * v^2
or, s = (mv^2) / 2F

Therefore, work done by the force,
W = Fs
or, W = F (mv^2) /2F
or, W = 1/2 mv ^2

hence,
kinetic energy = 1/2mv^2


hope it helps