Question

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

Answer 1

We know

`\\ \sf\longmapsto a=(dv)/(dt)`

`\\ \sf\longmapsto a=(dv)/(dx).(dx)/(dt)`

`\\ \sf\longmapsto a=v(dv)/(dx)`

`\\ \sf\longmapsto adx=vdv`

• Integrate

`\\ \sf\longmapsto a{\displaystyle{\int}^x_(x_0)}dx=\displaystyle{\int}_u^v vdv`

`\\ \sf\longmapsto a(x-x_0)=(v^2-u^2)/(2)`

Here

• x-x_0=s

`\\ \sf\longmapsto v^2-u^2=2as`