Question

Let $S_1$ and $S_2$ be the displacement in the first $(p-1)sec$ and $psec$ of a body moving from rest under constant acceleration. Find the displacement of the body in ${\left(p^2-p+1\right)}^{th}sec$ .

• 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 the second equation of motion we know that
$S=ut+\frac{1}{2}a{t}^2$
In $p-1$ seconds
$S_1=\frac{1}{2}a{\left(P-1\right)}^2$
and in $p$ seconds
$S_2=\frac{1}{2}a{P}^2$ [As $u=0$ ]
With above equations we know that
$S_1+S_2=\frac{1}{2}a(2p^2-2p+1)$

From the displacement formula of nth second we know that $S_n=u+\frac{a}{2}\left(2n-1\right)$
$S_{(P^2-P+1{)}^{th}}=\frac{a}{2}\left[2\left(P^2-P+1\right)-1\right]=\frac{a}{2}\left[2P^2-2P+1\right]$
It is clear that $S_{(P^2-P+1{)}^{th}}=S_1+S_2$