Question

A partical is moving in a straight line under constant acceletation. If the motion starts from rest, Find the ratio of displacement in `n` second to that in the `n^(th)` second.

Answer 1

`mu=0, a=a, t=n`
Displacement in n second
`s=ut+1/2at^(2)=0+1/2an^(2)=1/2an^(2) ...(i)`
Displacement in the `n^(th)` second
`s_(t)=u+1/2a(2t-1)`
`s_(n)=0+1/2a(2n-1) …(ii)`
`s/s_(n)=(1/2an^(2))/(1/2a(2n-1))=n^(2)/(2n-1)`