Question

a particle is falling freely under gravity. in first t seconds it cover s1 and next t second it covers s2 then t is given by

Answer 1

Answer:

t = √( (S₂ - S₁)/g )

Explanation:

a particle is falling freely under gravity. in first t seconds it cover s1 and next t second it covers s2 then t is given by

Let say Initial velocity = U  m/s

Acceleration = g  ( acceleration due to gravity as falling  freely)

Distance S = ut + (1/2)at²

Distance covered in t sec

S₁ = ut + (1/2)gt²

Distance covered in 2t sec

S₁ + S₂ = u2t +(1/2)g(2t)²

=> ut + (1/2)gt² + S₂ = 2ut + 2gt²

=> S₂ = ut + (3/2)gt²

S₂ - S₁ = gt²

=> t² = (S₂ - S₁)/g

=> t = √( (S₂ - S₁)/g )