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. $S_1/S_2$

Answer 1

Answer: (A)

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

$S_{(P^2-P+1{)}^{th}}=\frac{a}{2}[2(P^2-P+1)-1]$

$=\frac{a}{2}[2P^2-2P+1]$

It is clear that $S_{(P^2-P+1{)}^{th}}=S_1+S_2$