Derive the equation for uniform accelerated motion for the displacement covered in its `n^(th)` second of its motion. `(s_(n)=u+a(n-1/2))`

Explanation

We known that distance travelled by an object in t seconds is `s=ut+1/2at^(2)`
`therefore` Distance travelled in 'n' seconds, `s_((n sec))=un+1/2an^(2)" ".....(1)`
Distance travelled in (n - 1) seconds, `s_((n - 1))=u(n-1)+1/2a(n-1)^(2)" ".....(2)`
`therefore` Distance travelled in `n^(th)` second, `s_(n)=s_((nsec))-s_((n-1))sec`
= `(un+1/2an^(2))-[u(n-1)+1/2a(n-1)^(2)]`
`=cancel(un)+cancel(1/2an^(2))-cancel(un)+u-cancel(1/2an^(2))+1/cancel(2)a*cancel(2)n-1/2a=u+an-1/2a=u+a(n-1/2)`
`therefores_(n)=u+a(n-1/2)`