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
${S_1} + {S_2}$
${S_1}{S_2}$
${S_1} - {S_2}$
${S_1}/{S_2}$
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
From $S = ut + \frac{1}{2}a\;{t^2}$
${S_1} = \frac{1}{2}a{(P - 1)^2}$ and ${S_2} = \frac{1}{2}a\;{P^2}$ $[As\;u = 0$]
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[ {2{P^2} - 2P + 1} \right]$
It is clear that ${S_{{{({P^2} - P + 1)}^{th}}}} = {S_1} + {S_2}$
${S_1} = \frac{1}{2}a{(P - 1)^2}$ and ${S_2} = \frac{1}{2}a\;{P^2}$ $[As\;u = 0$]
From ${S_n} = u + \frac{a}{2}(2n - 1)$
${S_{{{({P^2} - P + 1)}^{th}}}} = \frac{a}{2}\left[ {2({P^2} - P + 1) - 1} \right]$
$ = \frac{a}{2}\left[ {2{P^2} - 2P + 1} \right]$
It is clear that ${S_{{{({P^2} - P + 1)}^{th}}}} = {S_1} + {S_2}$
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