A body starts from rest and moves for $n$ seconds with uniform acceleration $a$, its velocity after $n$ seconds is $v$ . The displacement of the body in last 3 seconds is:

Using $v=u+at$

$v=0+an$

$v=an$

$\Rightarrow a=\frac{v}{n}\dots \dots \left(1\right)$

Distance travelled in n seconds,

$s_n=un+\frac{1}{2}a{n}^2$

$s_n=0+\frac{1}{2}\left(\frac{v}{n}\right)n^2$

$s_n=\frac{1}{2}vn\mathrm{.....}\left(2\right)$

Distance travelled in (n-3) seconds,

$s_{n-3}=u(n-3)+\frac{1}{2}a{(n-3)}^2$

$s_{n-3}=0+\frac{1}{2}\left(\frac{v}{n}\right)(n^2+9-6n)$

$s_{n-3}=\frac{v}{2n}(n^2-6n+9)$

Displacement of body in last 3 seconds $=s_n-s_{n-3}$

$s=\frac{1}{2}vn-\frac{v}{2n}(n^2-6n+9)$

$s=\frac{vn}{2}-\frac{vn}{2}+\frac{6v}{2}-\frac{9v}{2n}$

$s=\frac{v}{2n}(6n-9)$