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Question

(C) Let the initial velocity be $u = 0$ and uniform acceleration be $a$.The distance covered in the $n^{	ext{th}}$ second is given by the formula: $S

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the initial velocity be $u = 0$ and uniform acceleration be $a$.The distance covered in the $n^{	ext{th}}$ second is given by the formula: $S_n = u + \frac{a}{2}(2n - 1)$.Since $u = 0$,$S_n = \frac{a}{2}(2n - 1)$.The total distance travelled in $n$ seconds is given by: $S_{total} = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}an^2 = \frac{1}{2}an^2$.The ratio of the distance covered in the $n^{	ext{th}}$ second to the total distance in $n$ seconds is:Ratio $= \frac{S_n}{S_{total}} = \frac{\frac{a}{2}(2n - 1)}{\frac{1}{2}an^2} = \frac{2n - 1}{n^2} = \frac{2n}{n^2} - \frac{1}{n^2} = \frac{2}{n} - \frac{1}{n^2}$.Thus,the correct option is $C$.

$A$ body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n^{\text{th}}$ second of its motion to the total distance travelled in $n$ seconds is

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