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Question

The relation between time and distance is t=αx2+βx, where α and β are constants. The retardation is

A
2αv3
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B
2βv3
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C
2αβv3
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D
2β2v3
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Solution

The correct option is A 2αv3
dtdx=2αx+βv=12αx+β
a=dvdt=dvdx.dxdt
a=vdvdx=12αx+β×2α(2αx+β)2
=2α(2αx+β)3=2α.v3
Retardation =2αv3

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