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Derivation of Position-Velocity Relation by Graphical Method

Two cars star...

Question

Two cars started moving with initial velocities $u$ and $2 u$ . For the same deceleration, their respective stopping distances are in the ratio

1 : 1

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1 : 2

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1 : 4

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2 : 1

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4 : 1

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Solution

The correct option is C $1 : 4$
$For the first car :$

Initial velocity = $u$
Final velocity = $0$
Deceleration = $a$
Using the equation of motion: $v^{2} = u^{2} - 2 a S$
$0 = u - 2 a S_{1}$
$\Rightarrow S_{1} = \frac{u}{2 a}$

$For the second car :$
Initial velocity = $2 u$
Final velocity = $0$
Deceleration = $a$
Using the equation of motion: $v^{2} = u^{2} - 2 a S$
$0 = {(2 u)}^{2} - 2 a S_{2}$
$\Rightarrow S_{2} = \frac{2 u}{a}$

$∴ \frac{S_{1}}{S_{2}} = \frac{\frac{u}{2 a}}{\frac{2 u}{a}}$
$∴ \frac{S_{1}}{S_{2}} = \frac{1}{4} = 1 : 4$

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Two cars started moving with initial velocities u and 2u. For the same deceleration, their respective stopping distances are in the ratio

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