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Derive the formula for kinetic energy.
Kinetic energy: The energy required or work done to move an object from one place to another is known as Kinetic energy. In other words, the energy possessed by a moving object is called Kinetic Energy. It is denoted by $K$ or $K.E.$ and in S.I. system its unit is joule.
Derivation of the Kinetic energy formula:
Let a Moving object of mass $m$ is in the state of the rest and with an external force $F$ and with and acceleration $a$ it moves with the velocity $v$ and it travels the $s$ distance.
Here, initial velocity $u=0$
On using equation of motion $v^2=u^2+2as$
Or $v^2=2as$
Or $a=\frac{v^2}{2s}$
Using Newton's force formula, $\overrightarrow{F}=m \overrightarrow{a}$
$F=m\times\frac{v^2}{2s}$
Or $F=\frac{1}{2s}mv^2$
Work done to move the object, $W=Force\times distance$
Therefore, $W=\frac{1}{2s}mv^2\times s$
Or $W=\frac{1}{2}mv^2$
And we know that the work done to move an object is called the Kinetic Energy.
Therefore, $\boxed{K=\frac{1}{2}mv^2}$
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