Speed of two identical cars are u and 4u at a specific instant and they are moving along straight paths with same retardation .The ratio of the respective distances in which the two cars are stopped from that instant is

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1 : 4

1 : 8

1 : 16

1 : 1

answer is D.

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Detailed Solution

Using $v^{2} = u^{2} + 2 as .$ If car is retarding and final velocity becomes zero. Then, the equation becomes.

$0 = u^{2} - 2 as \Rightarrow s = \frac{u^{2}}{2 a} or s \infty u^{2}$

As $s \infty u^{2} \Rightarrow \frac{s_{1}}{s_{2}} = {(\frac{1}{4})}^{2} = \frac{1}{16}$

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