Derivation for the distance travelled in the nth second , sn = u+( n-1/2)a .

S nth= u + 2a (2n-1)
In this problem, let us consider an object traveling with an initial velocity u and uniform acceleration a. Distance traveled in n seconds is given by Sn = un + 2 an2 (I)Distance traveled in (n-1) seconds is given by S sDistance traveled in nth second is n-1 = u (n-1) + a (n -1) 2 (II)
Snth = Sn -Sn-1 = un + s an2 -[u(n -1) + ss a(n-1)2 ] 2
= un + an2-[un-u + an-an + 21 a]
Ss(2n-1)nth = u + 2a (2n-1)