The relation between time and distance is t=αx2+βx where

Question -

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

Options:

A .

2 α v^{3}

B .

2 β v^{3}

C .

2 α β v^{3}

D .

2 β^{2} v^{3}

Answer: Option A
:
A

$\frac{d t}{d x} = 2 α x + β$

$\Rightarrow v = \frac{1}{2 α x + β}$

$∵ a = \frac{d v}{d t} = \frac{d v}{d x} . \frac{d x}{d t}$

$a = v \frac{d v}{d x} = \frac{- v .2 α}{(2 α x + β)^{2}} = - 2 α . v . v^{2} = - 2 α v^{3}$

$∴$ Retardation = $2 α v^{3}$

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