A particle starts from rest with uniform acceleration and is velocity after `n` seconds `v`. The displacement of the body in last two seconds is.

Options

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

Answer

D

Explanation

`because v = 0 + na rArr a = (v)/(n)`
Now, distance travelled in `n sec`
`rArr S_n = (1)/(2) an^2`
and distance travelled in `(n - 2) sec`
`rArr S_(n - 2) = (1)/(2) a(n - 2)^2`
`:.` Distance travelled in last two seconds
=`S_n - S_(n - 2)`
=`(1)/(2) an^2 - (1)/(2) a(n - 2)^2`
=`(a)/(2)[n^2 - (n - 2)^2]`
=`(a)/(2)[n + (n - 2)][n -(n - 2)]`
=`a(2 n - 2)`
=`(v)/(n)(2n - 2) = (2v(n - 1))/(n)`.