Question

Derive the equation of motion v²- u²= 2as​

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

Here we go ~

Let's use the given expression :

`\qquad \tt \dashrightarrow \:a = v (dv)/(ds)`

`\qquad \tt \dashrightarrow \:v \:dv= a \: {}{ds}`

Now, integrate both sides

`\qquad \tt \dashrightarrow \: \int_(u)^v (v )\: dv= {\int _(0 )^(s) }{}^{} (a) \: {}{ds}`

`\qquad \tt \dashrightarrow \: {\bigg[\frac{v {}^(2) }{2} \bigg]}_(u )^(v) \: = {\bigg[{a{s}^{} }{} \bigg]}_(0)^(s)`

`\qquad \tt \dashrightarrow \: (1)/(2) {\bigg[{v {}^(2) - {u}^(2) }{} \bigg]}_{}^{} \: = a{\bigg[{{s - 0}^{} }{} \bigg]}_{}^{}`

`\qquad \tt \dashrightarrow \: v {}^(2) - {u}^(2) =2 as`

`\qquad \tt \: \therefore v {}^(2) =u {}^(2) + 2as`

I hope you understood ~