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

Acceleratin of the block will be constat and let it be a. Block starts from rest.
`S_(n) = (1)/(2) an^(2) -(1)/(2)a(n -1)^(2) = (a)/(2)(2n-1)`
`(S_(n))/(S_(n+1)) = (2n-1)/(2n+1)`
Hence option (c) is correct.