Question

A car starts from rest and moves with constant accleration . The ratio of distance covered after n sec to the nth sec

Answer 1

Initial velocity = 0

acceleration = a

Distance covered in n seconds = 1/2 a t^2 = 1/2 an^2 = 0.5an^2


Distance travelled in nth second = 1/2×a[n^2 - (n-1)^2]
= 1/2×a[ n^2 - (n^2 -2n + 1)]
= 1/2×a [n^2 - n^2 + 2n - 1]
= 1/2×a [2n - 1]
= 0.5a(2n-1)


Ratio of distance travelled in n seconds and nth second is

$\frac{0.5a {n}^{2} }{0.5a(2n - 1)} = \frac{ {n}^{2} }{2n - 1}$