Question

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered in the $n^{th}$ second to distance covered in n seconds 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. $\frac{2}{n}+\frac{1}{n^2}$

Answer 1

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

We know,
$s_n=u+\frac{a}{2}(2n-1)=0+\frac{a}{2}(2n-1)$
$s=ut+\frac{1}{2}{at}^2=0+\frac{1}{2}{an}^2[\because t=nsec]$
$\therefore \frac{s_n}{s}=\frac{\frac{a}{2}(2n-1)}{{an}^2/2}=\frac{2}{n}-\frac{1}{n^2}$