A particle moving along a straight line with initial velocity u and acceleration a continues its motion for n seconds. What is the distance covered by it in the last `n^(th)` second ?

Explanation

`S=ut+1/2at^2`
Displacement in n seconds=`un+1/2an^2`
Displacement in (n-1) seconds
`=u(n-1)+1/2 a(n-1)^2`
Displacement in `n^(th)` second = Displacement in n seconds - displacement in (n-1) seconds
`therefore S_n=u+a(n-1/2)`