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 …….

A body initially at rest is moving with uniform acceleration "a". It's

1.	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 …….
Answer» `(V (n -1 ))/(n )` `(2n (n -1))/(n)` `( 2v (n -1))/(n)` `(2v (n -1))/(n)` Solution :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).