Motion In One Dimension Question 7
Question 7 - 2024 (29 Jan Shift 1)
A body starts moving from rest with constant acceleration covers displacement $S_{1}$ in first $(p-1)$ seconds and $\mathrm{S}{2}$ in first $\mathrm{p}$ seconds. The displacement $\mathrm{S}{1}+\mathrm{S}_{2}$ will be made in time :
(1) $(2 \mathrm{p}+1) \mathrm{s}$
(2) $\sqrt{\left(2 p^{2}-2 p+1\right) s}$
(3) $(2 \mathrm{p}-1) \mathrm{s}$
(4) $\left(2 p^{2}-2 p+1\right) s$
Show Answer
Answer: (2)
Solution:
$S_{1}$ in first $(p-1)$ sec
$\mathrm{S}_{2}$ in first $\mathrm{p}$ sec
$\mathrm{S}_{1}=\frac{1}{2} \mathrm{a}(\mathrm{p}-1)^{2}$
$\mathrm{S}_{2}=\frac{1}{2} \mathrm{a}(\mathrm{p})^{2}$
$\mathrm{S}{1}+\mathrm{S}{2}=\frac{1}{2} \mathrm{at}^{2}$
$(\mathrm{p}-1)^{2}+\mathrm{p}^{2}=\mathrm{t}^{2}$
$\mathrm{t}=\sqrt{2 \mathrm{p}^{2}+1-2 \mathrm{p}}$
