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The relation between time and distance is t = ${αx}^{2} + βx,$ where $α$ and $β are constants . The retardation is$

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2αv3

2βv3

2αβv3

2β2v3

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detailed solution

Correct option is A

dtdx = 2αx + β ⇒ v = 12αx+β∴ a = dvdt = dvdx.dxdta = vdvdx = -v.2α(2αx+β)2 = -2α.v.v2 = -2αv3 ∴ Retardation = 2αv3

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

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The relation between time and distance is t = ${αx}^{2} + βx,$ where $α$ and $β are constants . The retardation is$