Consider a particle moving with uniform acceleration ‘a’.Let u be the initial velocity of the particle.
Distance travelled during nth second = Distance travelled in ‘n’ seconds – Distance travelled in (n - 1) seconds
By the given condition 1/2 s = sn
gn2/4 = g(n - 1/2)
n2 - 4n + 2 = 0
n = (4 ± √(16 - 8))/2
n = 2 ± √2
∴ Time of the body’s fall = (2 ± √2)s