[tex]let \: us \: assume \: a \: body \: moving \: with \: \\ an \: initial \: velocity \: u \: . \: let \: its \: final \\ velocity \: be \: v \: after \: a \: time \: t \: and \: the \\ distance \: travelled \: by \: the \: body \: be \: s . \\ we \: already \: have \\ v = u + at.......(i) \\ s = \frac{u + v}{2} \times t..........(ii) \\ putting \: the \: value \: of \: t \: from \: (i) \: in \\ the \: equation \: (ii) \\ (v = u + at \\ or \: at = v - u \\ or \: t = \frac{v - u}{a} \\ now\\ s = \frac{u + v}{2} \times \frac{v - u}{a} \\ or \: s = \frac{ {v}^{2} - {u}^{2} }{2a} \\ or \: 2as = {v}^{2} - {u}^{2} \\ {v}^{2} = {u}^{2} + 2as \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
