A body is moving from rest under constant acceleration and let S1 be the&

Discussion Forum : Motion In One Dimension

Question -

A body is moving from rest under constant acceleration and let $S_{1}$ be the displacement in the first $(p - 1)$ seconds and $S_{2}$ be the displacement in the first $p$ seconds. The displacement in $(p^{2} - p + 1)^{t h}$ second will be

Options:

A .

S_{1} + S_{2}

B .

S_{1} S_{2}

C .

S_{1} - S_{2}

D .

\frac{S_{1}}{S_{2}}

Answer: Option A
:
A

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

$S_{1} = \frac{1}{2} a (p - 1)^{2}$ and $S_{2} = \frac{1}{2} a p^{2}$ [As u = 0]

We have

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

Using the expression for distance traveled in $n^{t h}$ second

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

$S_{(p^{2} - p + 1)^{t h}} = \frac{a}{2} [2 (p^{2} - p + 1) - 1] = \frac{a}{2} [2 p^{2} - 2 p + 1]$

It is clear that $S_{(p^{2} - p + 1)^{t h}} = S_{1} + S_{2}$

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