A body starts moving from rest with constant acceleration covers displacement S₁ in first (p-1) se

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2.Motion in Straight Line

hard

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

A $(2 \mathrm{p}+1)\ \mathrm{s}$

B $\sqrt{\left(2 \mathrm{p}^2-2 \mathrm{p}+1\right) }\ s$

C$(2 \mathrm{p}-1)\ \mathrm{s}$

D $\left(2 p^2-2 p+1\right)\ s$

(JEE MAIN-2024)

Solution

$S_1$ in first $(p-1) \mathrm{sec}$
$S_2$ in first $p$ sec
$ \mathrm{S}_1=\frac{1}{2} \mathrm{a}(\mathrm{p}-1)^2 $
$ \mathrm{~S}_2=\frac{1}{2} \mathrm{a}(\mathrm{p})^2 $
$ \mathrm{~S}_1+\mathrm{S}_2=\frac{1}{2} \mathrm{at}^2 $
$ (\mathrm{p}-1)^2+\mathrm{p}^2=\mathrm{t}^2 $
$ \mathrm{t}=\sqrt{2 \mathrm{p}^2+1-2 \mathrm{p}}$

Standard 11

Physics

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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

Solution

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