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 p sec. 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. $\frac{S_1}{S_2}$

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 $S_2=\frac{1}{2}a{P}^2$ $[Asu=0]$
From $S_n=u+\frac{a}{2}(2n-1)$
$S_{P^2-P+1}^{th}=\frac{a}{2}\left[2\right(p^2-P+1)-1]=\frac{a}{2}[2P^2-2P+1]$
It is clear that $S_{P^2-P+1}^{th}=S_1+S_2$