Question

question from kinematics

Answer 1

Distance covered in nth second:

S_(n) =u+a/2(2n-1) (1)

where the symbols have the usual meaning.

Also, from equations of motion,
distance covered in n seconds,

S=un+a/2×n^2 (2)

Dividing (1) by (2)

S_(n)/S =

$\frac{u + \frac{a}{2}(2n - 1) }{un + \frac{1}{2} an^{2} }$


As body starts from rest, u=0.

Thus,

S_(n)/S=
$\frac{ \frac{a}{2} (2n - 1)}{ \frac{a {n}^{2} }{2} }$


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

Answer 2

(2n-1):n
$(2n - 1)n ^{2}$