A body starts from rest and moves with uniform acceleration along a straight horizontal track. Let d₁ be the distance covered by the body in the p^ th second of its motion, and d₂ be the total distance covered by it in the first p seconds. The ratio d₁ d₂ is:

Step-by-step solution

Initial velocity u = 0 . Distance covered in the p^ th second is given by: d₁ = u + a 2 (2p - 1) = a 2 (2p - 1) Total distance covered in the first p seconds is given by: d₂ = up + 1 2 ap^2 = 1 2 ap^2 The ratio d₁ d₂ is: d₁ d₂ = a 2 (2p - 1) 1 2 ap^2 = 2p - 1 p^2 Answer: 2p-1 p^2