A body initially at rest is moving with uniform acceleration "a". It's velocity after n seconds is V. The displacement of the body in last 2 seconds is …….

Options

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

Answer

D

Explanation

Distance covered in `(n-2)` second,
`d _(n -2) = v _(0) (n -2) + 1/2 a (n-2) ^(2)`
`= v _(0) n = 2 v _(0) + 1/2 an ^(2) - 2an + 2a …(2)`
Subtracting equation (2) from equation (1),
`d _(n-2) = 2v _(0) + 2an -2a`
`v _(0) =0`
`therefoer d _(n) - d _(n-2) = 2a (n-1)...(3)`
Now, velocity is v in `n^(th)` second,
`therefore `in `v = v _(0) + an, ` putting `v_(0) =0,`
`v = an `
` therefore a = (v)/(n) ...(4)`
Putting value of equation (4) in equation (3), Distance covered in last 2 second,
`d _(n) - d _(n-2) = 2a (n-1)`
`= (2v (n-1))/(n)`
Which is option (B).