Answers

2014-08-24T15:04:21+05:30
Distance travelled = Area under the line
= ut + ½ (v-u)t
Acceleration (a) = (v-u)/t and so (v-u) = at
Therefore,
Distance travelled (s) = ut + ½ (v-u)t = ut + ½ (at)t = ut + ½ at²
Thus,proved.
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2014-08-25T05:47:02+05:30

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Acceleration is defined as change in velocity per unit time.
            =>   (v - u) / (t - 0)  = a        =>  v = u + at

Distance traveled is = average velocity * time duration

            S  = \frac{(initial + final velocity)}{2} * duration \\ \\ S = \frac{u + v}{2} * t   \\ \\ S = \frac{1}{2} (u + u + a t ) * t \\ \\ S = \frac{2ut + a t^2}{2} \\ \\ S = u t + \frac{1}{2} a t^2 \\ \\

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