Answer:
- [tex]{\boxed{\sf{\red{K.E = \frac{1}{2} mv^{2}}}}}[/tex]
Explanation:
[tex]{\underline{\underline{\bf{\orange{What \: is \: Kinetic\: Energy\:?}}}}}[/tex]
- The energy possessed by a body by virtue of its motion.
[tex]{\underline{\underline{\bf{\green{Formula\:Derivation\::-}}}}}[/tex]
[tex]\star\:\sf{Consider,}[/tex]
- Body of mass 'm' is moving with a velocity 'v'.
- A uniform force 'F' opposes the motion of a body and brings it to rest after a displacement 's'
[tex]:\implies\:\:\sf{v^{2} -u^{3} = 2a}[/tex]
[tex]:\implies\:\:\sf{0-v^{2} = 2as}[/tex]
[tex]:\implies\:\:\sf{-v^{2}=2as}[/tex]
[tex]:\implies\:\:\sf{a = \dfrac{-v^{2}}{2s}}[/tex]
The opposing force on the body,
By Newton's 3rd law, the force applied by the body :-
[tex]:\implies\:\:\sf{-F = -\bigg( -\dfrac{mv^2}{2s}\bigg) = \dfrac{mv^2}{2s}}[/tex]
[tex]{\boxed{\bf{W = Force \times Displacement}}}[/tex]
[tex]:\implies\:\:\sf{W = F \times S}[/tex]
[tex]:\implies\:\:\sf{W = \dfrac{mv^2}{2s}\times s = \dfrac{1}{2}mv^2}[/tex]
- We know that, Work done will be stored as kinetic energy in the body.
[tex]\star\:\:{\underline{\boxed{\sf{\red{K.E = \dfrac{1}{2}mv^{2}}}}}}[/tex]
