Question

A particle start from rest and moves with uniform acceleration the ratio of distance covered in nth second to n seconds is

Answer 1

Velocity at the end of (n-1) sec = U +at = 0+ a*(n-1)

Velocity at the end of n th sec = a*(n-1) + a*1 = na

Average velocity in the nth sec = (a*(n-1) + n*a) /2 = (a/2)(2n-1)

Distance covered in the n th sec =

Average velocity in the nth sec* time( =1) = (a/2)(2n-1)

Distance covered in n sec = 1/2 * a * t² = a/2 * n²

The desired ratio = (2n - 1) / n²