A particle moving in a straight line has velocity and displacement equation as V = 4 √ 1 + S , where V in m/s and s is in m. The initial velocity of the particle in m/s is ______ Options: A . &nbsp 7 B . &nbsp 8 C . &nbsp 9 D . &nbsp 4

Answer: Option D : D v = d s d t = 4 √ 1 + s ⇒ ∫ s o d s √ 1 + s = 4 ∫ t o d t ⇒ 4 t = 2 [ √ 1 + s − 1 ] ⇒ 2 t + 1 = √ 1 + s ⇒ 1 + s = 4 t 2 + 1 + 4 t ⇒ s = 4 t 2 + 4 t A t t = 0 s , s = 0 m ⇒ v | a t t = 0 s = 4 √ 1 + 0 = 4 m s − 1

A particle moving in a straight line has velocity and displacement equation as

Discussion Forum : Motion In One Dimension

Question -

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1 + S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

Options:

A . 7

B . 8

C . 9

D . 4

Answer: Option D
:
D

$v = \frac{d s}{d t} = 4 \sqrt{1 + s} \Rightarrow \int_{o}^{s} \frac{d s}{\sqrt{1 + s}} = 4 \int_{o}^{t} d t \Rightarrow 4 t = 2 [\sqrt{1 + s} - 1] \Rightarrow 2 t + 1 = \sqrt{1 + s} \Rightarrow 1 + s = 4 t^{2} + 1 + 4 t \Rightarrow s = 4 t^{2} + 4 t A t t = 0 s, s = 0 m \Rightarrow v |_{a t t = 0 s} = 4 \sqrt{1 + 0} = 4 m s^{- 1}$

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Discussion Forum : Motion In One Dimension

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