Q. A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the $n$th second to the distance covered in $n$ second 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) $\frac{2}{n} + \frac{1}{n^{2}}$
Explanation
(a) Here, $s_{n} = \frac{1}{n}an^{2}$
$s_{nth}$ = distance travelled in $n$ second – distance travelled in $(n - 1)$ second
$= \left( \frac{2n - 1}{2} \right)a$
$\therefore\ \frac{s_{nth}}{s_{n}} = \frac{2n - 1}{n^{2}} = \frac{2}{n} - \frac{1}{n^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.