Question

Derive an equation for the distance covered by a uniformly accelerated body in the n^th second of its motion. A body travels half its total path in the last second of its fall from rest. Calculate the time of its fall.

Answer 1

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 = s_n

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