Q 11-02-065JEE MainJEE Main 2024 (29 Jan, Shift 1)Medium
A body starts moving from rest with constant acceleration and covers displacement $S_1$ in first $(p-1)$ seconds and $S_2$ in first $p$ seconds. The displacement $S_1 + S_2$ will be made in time:
Answer: (B) $\sqrt{2p^2 - 2p + 1}\ \text{s}$
From rest, $S = \frac12 at^2$:
$$S_1 = \frac12 a(p-1)^2,\qquad S_2 = \frac12 ap^2$$
If $S_1 + S_2$ is covered in time $t$:
$$\frac12 at^2 = \frac12 a\left[(p-1)^2 + p^2\right] \;\Rightarrow\; t = \sqrt{2p^2 - 2p + 1}\ \text{s}$$
Solution by Sreeraj P, M.Sc Physics