Two trains are moving with velocities $v_{1} = 10 m s^{- 1}$ and $v_{2} = 20 m s^{- 1}$ on the same track in opposite directions. After the application of brakes if their retarding rates are $a_{1} = 2 m s^{- 2}$ and $a_{1} = 1 m s^{- 2}$ respectively, then the minimum distance of separation between the trains to avoid collision is

150 m

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225 m

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450 m

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300 m

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Solution

The correct option is B $225 m$
the minimum distance must be the distance for both trains to come at rest
$v^{2} = u^{2} + 2 a_{1} s_{1}$
$0 + 100 - 4 s_{1}$
$s_{1} = 25 m$

for train 2
$0 = 400 - 2 a_{2} s_{2}$
$s_{2} = 200 m$
therefore the minimum distance is 225 m

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