Question

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 $psec.$ The displacement in $(p^{2} - p + 1)^{th}$ sec. will be

• A. $S_{1} + S_{2}$
• B. $S_{1}S_{2}$
• C. $S_{1} - S_{2}$
• D. $S_{1}/S_{2}$

Answer 1

Answer: (A)

$S_{1} + S_{2}$

Answer 2

From $S = ut + \frac{1}{2}a\mspace{6mu} t^{2}$

$S_{1} = \frac{1}{2}a(P - 1)^{2}$ and $S_{2} = \frac{1}{2}a\mspace{6mu} P^{2}$ $\lbrack As\mspace{6mu} u = 0$]

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

$S_{(P^{2} - P + 1)^{th}} = \frac{a}{2}\left\lbrack 2(P^{2} - P + 1) - 1 \right\rbrack$ $= \frac{a}{2}\left\lbrack 2P^{2} - 2P + 1 \right\rbrack$

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