A body starts moving from rest with constant acceleration covers displacement in first seconds and in first seconds. The displacement will be made in time

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Solution

Q.
A body starts moving from rest with constant acceleration 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 [2024]

1 $(2 p + 1) s$

2 $\sqrt{(2 p^{2} - 2 p + 1)} s$

3 $(2 p - 1) s$

4 $(2 p^{2} - 2 p + 1) s$

Ans.
(2)

The displacement $S_{1}$ in first $(p - 1)$ sec, $S_{1} = \frac{1}{2} a {(p - 1)}^{2}$

The displacement $S_{2}$ in first $p$ sec, $S_{2} = \frac{1}{2} a {(p)}^{2}$

   $S_{1} + S_{2} = \frac{1}{2} a t^{2}$

   ${(p - 1)}^{2} + p^{2} = t^{2} \Rightarrow t = \sqrt{2 p^{2} + 1 - 2 p}$

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