A body moves from rest under constant acceleration. Let S₁ be the displacement in the first (p-1) s and S₂ the displacement in the first p s. The displacement in the (p²-p+1)th second is:
Options

Question

A body moves from rest under constant acceleration. Let S₁ be the displacement in the first (p-1) s and S₂ the displacement in the first p s. The displacement in the (p²-p+1)th second is:

G1 Physics · Accepted Answer

From rest, S₁=(a/2)(p-1)² and S₂=(a/2)p². Their sum is (a/2)(2p²-2p+1). The displacement in the n-th second is (a/2)(2n-1). For n=p²-p+1 this is the same quantity. Hence required displacement = S₁+S₂, option A.