A body is moving from rest under constant acceleration and let S₁ be the displacement in the first (p – 1) sec and S₂ be the displacement in the first p sec. The displacement in (p² – 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 $S = u t + \frac{1}{2} a t^{2}$

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

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

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

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

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

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