Question

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

Answer: (A)

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

Distance travelled by a body in '$n$'th second is
$s_n=u+\frac{a}{2}(2n-1)$
Distance travelled in 'n' seconds is
$s=un+\frac{1}{2}a{n}^2$
$u$ is zero since the body starts from rest.
$\frac{s_n}{s}=\frac{\frac{a}{2}(2n-1)}{\frac{1}{2}a{n}^2}$
Therefore, the ratio = $\frac{s_n}{s}=\frac{2}{n}-\frac{1}{n^2}$