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A body is moving from rest under constant acceleration and let $S_{1}$ be the displacement in the first (p-1) sec and $S_{2}$ be the displacement in the first p sec. The displacement in ${(p^{2} - p + 1)}^{th} \sec . will be$

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$S_{1} + S_{2}$

$S_{1} S_{2}$

$S_{1} - S_{2}$

$S_{1} / S_{2}$

answer is A.

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Detailed Solution

From S = ut + $\frac{1}{2} {at}^{2}$

$S_{1} = \frac{1}{2} a {(P - 1)}^{2} and S_{2} = \frac{1}{2} a P^{2} [As u = 0]$

From $S_{n} = u + \frac{a}{2} (2 n - 1)$

$S_{{(P^{2} - P + 1)}^{th}} = \frac{a}{2} [2 (P^{2} - P + 1) - 1]$

= $\frac{a}{2} [2 P^{2} - 2 P + 1]$

It is clear that $S_{{(P^{2} - P + 1)}^{th}} = S_{1} + S_{2}$

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