A body is moving from rest under constant acceleration and let S_{1} be the displacement in the first \(\left( p - 1 \right)\) sec and S_2 be the displacement in the first p sec. The displacement in \(\left(p^{2} + p + 1\right)^{th}\) sec. will be
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From \(S = ut + \frac{1}{2} a t^{2}\)
\(S_1 = \frac{1}{2} a (P - 1)^2\) and \(S_2 = \frac{1}{2} a P^2\) [Asu] = 0 ]
From \(S_n = u + \frac{a}{2} (2n - 1)\)
\(S_{(P^{2} - P + 1)}^{th} = \frac{a}{2} \left[ 2(P^{2} - P + 1) - 1 \right]\) \(= \frac{a}{2} \left[ 2P^{2} - 2P + 1 \right]\)
It is clear that S_{(P^{2} - P + 1)}^{th} = S_{1} + S_{2}
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