During n th second of its motion of a body covers a distance Sn with uniform acceleration 'a' and initial velocity 'u'. Show that, a =2Sn/2n-1 - 2u/2n-1

Let the total time of motion be t then u =initial velocity, and a =acceleration

distance travelled in in t seconds will be

Dt = u t + ½ a t^2

D(t-1) = u(t – 1) + ½ a (t-1)^2

distance travelled in 1 sec less from total time 

Distance travelled in nth sec = Sn = Dt – Dt-1 = u + ½ a (2t – 1)

thus

a = 2(Sn – u) / 2n – 1