First slide

Rectilinear Motion

Question

A body starts from rest and moves with constant acceleration the ratio of the distance covered in the nth second to that covered in ‘n’ seconds is

Moderate

A

$\frac{2}{n^{2}} + \frac{1}{n}$
B

$\frac{2}{n^{2}} - \frac{1}{n}$
C

$\frac{2}{n} + \frac{1}{n^{2}}$
D

$\frac{2}{n} - \frac{1}{n^{2}}$

Solution

Given that $u = 0$
$∴$ The distance travelled in the nth second is
$S_{n} = u + a (n - \frac{1}{2})$
$S_{n} = 0 + a (2 n - 1) ......... (i)$
The distance travelled in seconds is
$\begin{array}{l} S = u (n) + \frac{1}{2} a (n)^{2} \\ S = \frac{1}{2} a (n)^{2} \dots \dots \dots . (i i) \\ ∴ \frac{S n}{S} = \frac{\frac{(2 n - 1) a}{2}}{a (\frac{n^{2}}{2})} = \frac{(2 n - 1)}{n^{2}} = \frac{2}{n} - \frac{1}{n^{2}} \end{array}$

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