Question

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the $n^{th}$ sec to the distance covered in $nsec$ is:

• 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. $\frac{1}{n}-\frac{1}{n^2}$

Answer 1

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

It is given that $u=0$

Distance covered in $n$ seconds = $un+\frac{1}{2}a{n}^2$

$=\frac{a{n}^2}{2}$

Distance covered in $(n-1)$ seconds=$\frac{1}{2}a(n-1{)}^2$

Thus distance covered in $n^{th}$ second = $s_n-s_{n-1}$

$=\frac{a}{2}[n^2-(n-1{)}^2]$

Thus ratio of the distance covered in the $n^{th}$ sec to the distance covered in $n$ sec is $\frac{n^2-(n-1{)}^2}{n^2}$

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