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Two cars C(1) and C(2) moving in the sam...

Two cars `C_(1)` and `C_(2)` moving in the same direction on a straight single lane road with velocities `v_(1)=12 m s^(-1)` and `v_(2) =10 m s^(-1)`, respectively . When the separation between the two was `d=200 m`, `C_(2)` started accelerating to avoid collision. What is the minimum acceleration of car `C_(2)` so that they do not collide?
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Text Solution

Verified by Experts

By relative
`veca_(C_(1)C_(2))=veca_(C_(1)-veca_(C_(2))=0-a=(-a)`
`vecV_(C_(1)C_(2))=vecV_(C_(1))-vecV_(C(2))=12-10=2m//s`
So by relativity we want the car to stop.
`:. V^(2)-u^(2)=2as`.
` rArr 0-2^(2)=-2xxaxx200`
`rArra=1/(100)m//s^(2)=0.1m//s^(2)=1cm//s^(2)`.
`:."Minimum acceleration needed by car"C_(2)=1 cm//s^(2)`.
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