Question

A body starts from rest under constant acceleration and let $S_1$ be the displacement in the first $(p-1)$ seconds and $S_2$ be the displacement in the first $p$ seconds. The displacement in $(p^2-p+1{)}^{th}$ second will be

• A. $S_1+S_2$
• B. $S_1{S}_2$
• C. $S_1-S_2$
• D. $S_1/S_2$

Answer 1

The correct option is A $S_1+S_2$

From $S=ut+\frac{1}{2}a{t}^2$
$S_1=\frac{1}{2}a(p-1{)}^2$ and $S_2=\frac{1}{2}a{p}^2[\text{as}u=0]$
From $S_n=u+\frac{a}{2}(2n-1)$,
Distance travelled in $(p^2-p+1{)}^{th}$ second,
$S_{(p^2-p+1{)}^{th}}=\frac{a}{2}\left[2\right(p^2-p+1)-1]$
$=\frac{a}{2}[2p^2-2p+1]$ [as $u=0$]
It is clear that $S_{(p^2-p+1{)}^{th}}=S_1+S_2$