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. $S_1S_2$
• C. $S_1 - S_2$
• D. $S_1/S_2$

Answer 1

Answer: (A)

From $S = ut + \frac{1}{2} at^2$
$S_1 = \frac{1}{2} a(P - 1)^2$
and $S_2 = \frac{1}{2} aP^2$ [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 $S_{(P^2 - P + 1)^{th}} = S_1 + S_2$