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A train starts from station $A$ with uniform acceleration $a_{1}$ for some distance and then goes with uniform retardation $a_{2}$ for some more distance to come to rest at station $B .$ The distance between stations $A$ and $B$ is $4 k m$ and the train takes $\frac{1}{15} h$ to complete this journey $.$ If accelerations are in $k m$ per square minute $,$ then the value of $\frac{1}{a_{1}} + \frac{1}{a_{2}}$ in suitable unit is $_______.$

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$6$

$2$

$9$

$4$

answer is B.

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Detailed Solution

Using velocity - time graph of the train

$t_{1} + t_{2} = \frac{1}{15} h = 4 m i n$

$v = a_{1} t_{1} = a_{2} t_{2}$

$s = \frac{1}{2} (t_{1} + t_{2}) v \Rightarrow 4 = 2 v$

$t_{1} + t_{2} = v [\frac{1}{a_{1}} + \frac{1}{a_{2}}] \Rightarrow 4 = 2 [\frac{1}{a_{1}} + \frac{1}{a_{2}}]$

$\Rightarrow \frac{1}{a_{1}} + \frac{1}{a_{2}} = 2$

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