A body starts moving from rest with constant acceleration covers displacement S₁ in first (p-1) seconds and S₂ in first p seconds. The displacement S₁+S₂ will be made in time :

Solution

Physics sir · 4 steps

From rest, displacement grows as t², so add the squares of the times, not the times themselves.

1. Displacement from rest. With u = 0 and constant acceleration a, the displacement in the first t seconds is S = 1/2at².
2. Write both displacements. S₁ = 1/2a(p-1)² and S₂ = 1/2ap².

   1/2at² = 1/2a(p-1)² + 1/2ap²

3. Cancel and expand. The 1/2a cancels, so t² = (p-1)² + p² = p² - 2p + 1 + p² = 2p² - 2p + 1.
4. So. t = √(2p² - 2p + 1) s, which is option (d).

The idea to keep. For a body starting from rest, S ∝ t². To find the time for a combined distance, add the t² values and take the square root at the end.

Answer from the NTA final answer key. Solution by PrepWiser.