A small block slides without friction down an iclined plane starting form rest. Let `S_(n)` be the distance traveled from time `t = n - 1` to `t = n`. Then `(S_(n))/(S_(n + 1))` is:

Options

A. `(2n - 1)/(2n)`
B. `(2n + 1)/(2n - 1)`
C. `(2n - 1)/(2n + 1)`
D. `(2n)/(2n + 1)`

Answer

C

Explanation

Distance travelled in `t^(th)` second is,
`s_(t) = u + at - (1)/(2) a`
Given : `u = 0`
`:gt (S_(n))/(S_(n + 1)) = (an - (1)/(2) a)/(a (n + 1) - (1)/(2) a) = (2n - 1)/(2n + 1)`
Hence, the correct option is (c)