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Physics Part I

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Class 10 Class 12
Two trains are heading towards each other on the same straight track with speed 15 m/sec and 10 m/sec. When they are 250 m apart the drivers of both the trains apply their brakes. If one train retards at the rate 0·5 m/s2 then what should be the retardation of the second train so that collision of two trains just averts?

Given, two trains are heading towards each other on the same straight track. 



Initial relative speed of two trains,

straight u subscript straight r equals 15 plus 10 space equals space 25 space straight m divided by sec

Let 'a' be the retardation of second train.

Therefore the relative retardation is,

space space straight A equals left parenthesis straight a plus 0.5 right parenthesis space straight m divided by straight s squared

The collision will just avert if the relative speed of the two trains just becomes zero after travelling the distance of 250m.

Now,       space space space space straight v subscript straight r superscript 2 minus straight u subscript straight r superscript 2 space equals space 2 AS

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rightwards double arrow                625 space equals space 500 left parenthesis straight a plus 0.5 right parenthesis

rightwards double arrow                   straight a equals 0.75 space straight m divided by straight s squared 

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