Speeds of two identical cars are $u$ and $4 u$ at a specific instant. If the same deceleration is applied on both the cars, the ratio of the respective distances in which the two cars are stopped from that instant is

1 : 1

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1 : 4

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1 : 8

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1 : 16

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Solution

The correct option is D $1 : 16$
Both are given the same deceleration simultaneously and both finally stop.
Formula relevant to motion : $u^{2} = 2 a s$
$∴$ For first car, $s_{1} = \frac{u^{2}}{2 a}$
For second car, $s_{2} = \frac{(4 u)^{2}}{2 a} = \frac{16 u^{2}}{2 a}$
$∴ \frac{s_{1}}{s_{2}} = \frac{1}{16}$

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