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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, $\boxed{K=\frac{1}{2}mv^2}$