Question

$Derive \: the \: equation \: \: s = ut + \frac{1}{2} a {t}^{2} for \: position - time \: relation \: \ \textless \ br /\ \textgreater \ for \: an \: object \: travelling \: under \: uniform \: acceleration \: on \: a \: \ \textless \ br /\ \textgreater \ straight \: path.$
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Answer 1

Explanation:

$let \: us \: consider \: a \: body \:</p><p> of \: mass \: m</p><p> \: covers \: a \: distance \: s \: \\ let \: at \: time \: t \: = 0 \: its \: initial \: velocity \: is \: u \: </p><p>and \: at \: time \: t \: = t \: it \: acquires \: </p><p>final \: velocity \: v</p><p> \\ \\ now \: we \: know \\ v \: = \frac{ds}{dt} \\ ds \: = vdt \: \: - - - (1) \\ \\ integrating \: equation \: (1) \: we \: get \: \\ and \: using \: v \: = u \: + at \\ \\ s \: = \: ut \: + \: \frac{1}{2} a {t}^{2}$