Question

Define Kinetic Energy and derive the expression for it.

Answer 1

The energy by virtue of motion is called as kinetic energy. An object that has motion, whether it may be vertical or horizontal motion, has kinetic energy. Kinetic energy depends on mass($m$) of the object and speed ($v$) of the object.

The equation used to represent kinetic energy is:
$KE=\frac{1}{2}m{v}^2$
Derivation of kinetic energy :-
Work done by the force is given by,

$W=F.s$

where $F$ is the force and $s$ is the displacement in the direction of the force.

We know that, $F=ma$
Therefore, $W=m.a.s$ -------(1)
From the equation of motion, we have,
$v^2-u^2=2as$
As the body was initially at rest so u = 0
Therefore, $\frac{1}{2}{v}^2$ $=as$ ------- (2)
Putting the value of '$as$' from eqn.(2) into eqn.(1) we get,
$W=\frac{1}{2}m{v}^2$
This work done by the force gets used to increase the kinetic energy of the body.
Therefore, $KE=\frac{1}{2}m{v}^2$.