Question

Kinematics.
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Answer 1

here is your answer ⤵️

t=αx² +βx

differentiate on both side with time..

$\frac{dt}{dt} = 2 \alpha x \times \frac{dx}{dt} + \: \beta \times \frac{dx}{dt}$

$1 = 2 \alpha xv + \beta v$

$1 = v(2 \alpha x + \beta )$

$\frac{1}{v} = 2 \alpha x + \beta$

$2 \alpha x + \beta = \frac{1}{v}$

again differentiate both side with time,,

$2 \alpha \times \frac{dx}{dt} = \ - {v}^{2} \times \frac{dv}{dt}$

$2 \alpha v = {v}^{ - 2} .accelration$

$accelration = { - 2 \alpha v}^{3}$

negative sign indicate retardation therefore,,,

retardation = 2αv³

Hence, option (a) is the correct answer.

__hope it help ✌️