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

Answer

b

Explanation

Displacement in `n^(th)` second can be written as follows:
`S_(n)=(1)/(2)a(2n-1)`
Hence we can write
`S_(n+1)=(1)/(2)a[2(n+1)-1]=(1)/(2)a(2n+1)`
`(S_(n))/(S_(n+1))=(2n-1)/(2n+1)`