A body iniitially at rest is moving with uniform acceleration a. Its velocity after n seconds is v. The displacement of the body in last 2 s is

Options

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

Answer

A

Explanation

`u = 0`,. acceleration `= 0`
`t = n sec`,
The velocity after `n sec` is
`V = u + at`
`V = 0 + a(n)`
`V = an`
`a = (V)/(n)"........."(i)`
the displancement of the body in the last two seconds `[S = ut + (1)/(2) at^(2) = (1)/(2) at^(2)]`
`S_(2) = S_(n) - S_(n-2)`
`(1)/(2)an^(2) - (1)/(2)a(n-2)^(2) = (1)/(2)a[n^(2) - (n - 2)^(2)]`
`= (1)/(2) a[n^(2) - n^(2) - 4 + 4n]`
`S_(2) = 2a(n-1)`
From equation (i) `S_(2) = (2V(n-1))/(n)`
Alitar :

`BC = ? `
`BC = AC - AB`
`= [0 xx n + (1)/(2)an^(2)] - (0 xx (n - 2) + (1)/(2)a (n - 2)^(2))`.
`BC = (a)/(2) [n^(2) - n^(2) - 4 + 4n] = (4a)/(2)[n-1]`
`BC = 2a(n-1)"......."(1)`
For `AC`
`V = u + at`
`V = 0 + an`
`a = (V)/(n) .......(2)`
From `(1)` and `(2)`
`BC = (2V)/(n) (n - 1)`