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. $\frac{S_1}{S_2}$
• D. $S_1$ $S_2$

Answer 1

The correct option is A

$S_1$ + $S_2$

Formula Used: $S=ut+\frac{1}{2}a{t}^2$

From second equation of motion $S=ut+\frac{1}{2}a{t}^2$

Displacement in first $(P-1)sec$

$S_1=\frac{1}{2}a(P-1{)}^2$

Displacement in first $Psec$
$S_2=\frac{1}{2}a{P}^2$ [As $u=0$]

As displacement in $n^{th}sec$

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

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

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

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