Question

derive the expression of the following kinetic energy and potential energy

Answer 1

the energy possed by an object due to its motion is called kinetic energy.
the energy possessed by an object because of its position or shape is called potential energy.

Answer 2

Expression for kinetic energy =
According to Newton's second law of motion
F = ma ____(i)
As W = F. S
=(ma)S ____(ii)
According to third equation of motion v
v²-u²=2as ______(iii)
As the object starts from rest. u=0
Putting this value in equation (iii)
v²-u²=2as
v²-0=2as
It implies S=v²/2a
Putting this value in equation (ii)
W=(ma) S
=ma×v²/2a
=1/2mv²
We know,
Work done is equal to the kinetic energy of the body.
Thus K. E. =1/2mv²

Expression for potential energy =
According to Newton's second law of motion
F=ma
If the body is raised to same height h,
Then F=mg(weight)
and the displacement is h
W = force ×displacement
W=mgh.
This worked done against force of gravity is equal to potential energy or gravitational potential energy of the object.
Thus P. E. =mgh