Question

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the nth second to the distance covered in n second

• A. $\frac {2}{n} - \frac {1}{n^2}$
• B. $\frac {1}{n^2} - \frac {1}{n}$
• C. $\frac {2}{n^2} - \frac {1}{n^2}$
• D. $\frac {2}{n} + \frac {1}{n^2}$

Answer 1

Answer: (A)

$S_{n}=u+\frac{a}{2}(2 n-1)$
(Distance travelled in nth second
or $S_{n}=0+\frac{a}{2}(2 n-1) \dots$(i)
also. $S =u t+\frac{1}{2} a t^{2} $
$=0+\frac{1}{2} a n^{2} \dots$(ii)
(Distance travelled in $n$ th second)
$\therefore \frac{S_{n}}{S}=\frac{\frac{a}{2}(2 n-1)}{a n^{2} / 2}$
$=\frac{2}{n}-\frac{1}{n^{2}}$