Q. 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 $\left( P^{2} - P + 1 \right)^{th}$ see will be
A) $S_{1} + S_{2}$
B) $S_{1}S_{2}$
C) $S_{1} - S_{2}$
D) $S_{1}\ /\ S_{2}$
Explanation
(a) From the equation of motion
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ S = ut + \frac{1}{2}\ at^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ S_{1} = 0 + \frac{1}{2}\ a(P - 1)^{2}$
And $\ \ \ \ \ \ \ S_{2} = 0 + \frac{1}{2}\ aP^{2}$
From $\ \ \ \ S_{n} = u + \frac{a}{2}(2n - 1)$
$S_{\left( P^{2} - P + 1 \right)^{th}} = \frac{a}{2}\left\lbrack 2\left( P^{2} - P + 1 \right) - 1 \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{a}{2}\left\lbrack 2P^{2} - 2P + 1 \right\rbrack = S_{1} + S_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.