What’s kinetic energy?
kinetic energy possessed by a body due to it`s motion . It is the energy of motion . when you are walking or running your body is exhibiting kinetic energy . A bicycle or skateboard in motion possesses kinetic energy .Running water has kinetic energy and it is used to run water mills .Moving air has K.E and is used to derives wind mills and pushes sailing boats , similarly a bullet fired from a gun has kinetic energy and can penetrate into a target because of its K.E . Remember, kinetic energy is the energy of motion . The faster the body move,s the more the kinetic energy is formed as a process of movement . for example , when a bus speeds up going down a hill, the potential energy of bus converts into K.E . There is not much potential energy at the bottom of the hill , but there is a great amount of kinetic energy .Similarly a basket ball shows kinetic energy ,the K.E is proportional to the balls mass and square of its velocity . to throw the same ball twice as fast , a player does more work and transfers four times the energy . formula of kinetic energy is given by
where m is the mass of the body moving with velocity v . unit of kinetic energy is joule . if the mass is given in kilogram and velocity v is given in meter/second then kinetic energy comes out in joules . one joule is the energy when a force of one newton displaces a body through one meter .
What happens when the velocity is increased by keeping the weight constant?
It mean if we increase the velocity of an object two times its kinetic will increase four times,if we increase the velocity three times its kinetic energy will increase nine times,if we increase the velocity 4 times its kinetic energy will increase sixteen times and so on..
Types of k.E:

Heat energy:
Heat is a form of energy given out by hot bodies.Large amount of heat is obtained by burning fuel.Heat is also produced when motion is opposed by frictional forces.The foods we take provide us heat energy.The sun is the main source of heat energy.

Electrical energy:
Electricity is one of the widely used forms of energy.Electrical energy can be supplied easily to any desired place through wires .We get electrical generators.These electric generators are run by hydro power,thermal power or nuclear power.

Sound energy:
When you knock at the door,you produce sound.Sound is a form of energy.It is produced when a body vibrates ;such as vibrating diaphragm of a drum,vibrating strings ,of a sitar and vibrating air column of wind instruments such as flute pipe etc..

Light energy:
Light is a form of energy.The sun is the major source of light for us.Light helps plants to make food in the process of photosynthesis.
Derivation of the formula of k.E:
Let a force F moves a body from
V_{i=}0 to v_{f=}v
And a body covers a distance S in its direction.We know that:
W = FS …..(1)
But
F = ma
And we also have a relation:
2as = V_{f }^{2}– V_{i}^{2 }…..(2)
By putting values of v_{i=0} and v_{f=}v we get:
2as = (v)^{2 }–(0)^{2}
2as = v^{2}…….(3)
We also know that:
F=ma
a=F/m
put value of a in equation (3) then we will get:
2(F/m)s=V^{2}
By rearranging above equation we will get:
FS = ½ mV^{2 }….(4)
But we know that FS=W so equation (4) will become as:
W=1/2 mV^{2}
Because this work done on the body of mass m will set the body moving with velocity v from its state of rest,it is equal to kinetic energy of the body.So:
K.E=1/2 mV^{2}
Video of Derivation of K.E:
See also Nuclear energy which is also type of potential energy.
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