Question

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

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

Answer 1

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

As body starts from rest, therefore $u=0$

Distance covered in $n^{th}$ second is given by
$S_n=u+\frac{a}{2}(2n-1)$

$S_n=\frac{a}{2}(2n-1)$

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

So, $\frac{S_n}{S}=\frac{2n-1}{n^2}$