Answered

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please someone derive 3rd equation of motion u- v= 2sa​

Sagot :

We know

[tex]\\ \sf\longmapsto a=\dfrac{dv}{dt}[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{dv}{dx}.\dfrac{dx}{dt}[/tex]

[tex]\\ \sf\longmapsto a=v\dfrac{dv}{dx}[/tex]

[tex]\\ \sf\longmapsto adx=vdv[/tex]

  • Integrate

[tex]\\ \sf\longmapsto a{\displaystyle{\int}^x_{x_0}}dx=\displaystyle{\int}_u^v vdv[/tex]

[tex]\\ \sf\longmapsto a(x-x_0)=\dfrac{v^2-u^2}{2}[/tex]

Here

  • x-x_0=s

[tex]\\ \sf\longmapsto v^2-u^2=2as[/tex]

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