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 $psec$. The displacement in $(p^2-p+1{)}^{n}sec$. 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)

$S_1+S_2$

The initial velocity of body is zero, $u=0$

2rd equation of motion,

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

$S=\frac{1}{2}a{t}^2$. . . . . .. .(1)

The displacement in time $(P-1)$ sec is

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

The displacement at time $P$ sec,

$S_2=\frac{1}{2}a{P}^2$. . . . . .(3)

Adding equation (2) and (3), we get

$S_1+S_2=\frac{1}{2}a(2P^2-2P+1)$. . . . . .(4)

The displacement at time $(p^2-P+1{)}^{n}sec$

$S=\frac{1}{2}a(2P^2-2P+1)$. . . . .(5)

From equation (4) and (5),

$S=S_1+S_2$

The correct option is A.