Question

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the $n^{th}$ second to the distance covered in $n$ seconds is given by

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

Answer 1

The correct option is A $\frac{2}{n}-\frac{1}{n^2}$

Distance traveled in n seconds
$s=\frac{1}{2}a{n}^2$
Distance traveled in $n^{th}$ second
$s_{n^{th}}=\frac{1}{2}a{\left(n\right)}^2-\frac{1}{2}a{(n-1)}^2$
$\Rightarrow s_{n^{th}}=\frac{1}{2}a(2n-1)$
$\frac{s_{n^{th}}}{s_n}=\frac{2n-1}{n^2}=\frac{2}{n}-\frac{1}{n^2}$