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)