[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
Let's use the given expression :
[tex]\qquad \tt \dashrightarrow \:a = v \dfrac{dv}{ds} [/tex]
[tex]\qquad \tt \dashrightarrow \:v \:dv= a \: {}{ds} [/tex]
Now, integrate both sides
[tex]\qquad \tt \dashrightarrow \: \int_{u}^v (v )\: dv= {\int _{0 }^{s} }{}^{} (a) \: {}{ds} [/tex]
[tex]\qquad \tt \dashrightarrow \: {\bigg[\dfrac{v {}^{2} }{2} \bigg]}_{u }^{v} \: = {\bigg[{a{s}^{} }{} \bigg]}_{0}^{s}[/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{1}{2} {\bigg[{v {}^{2} - {u}^{2} }{} \bigg]}_{}^{} \: = a{\bigg[{{s - 0}^{} }{} \bigg]}_{}^{}[/tex]
[tex]\qquad \tt \dashrightarrow \: v {}^{2} - {u}^{2} =2 as[/tex]
[tex]\qquad \tt \: \therefore v {}^{2} =u {}^{2} + 2as[/tex]
I hope you understood ~
