First slide

Instantaneous acceleration

Question

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

Moderate

A

$2 {αv}^{3}$
B

$2 β v^{3}$
C

$2 α β v^{3}$
D

$2 b^{2} v^{3}$

Solution

$t = α x^{2} + β x Differentiating: 1 = 2 α \frac{dx}{dt} x + β \frac{dx}{dt} ∣ v = \frac{dx}{dt} = \frac{1}{β + 2 αx}; \frac{dv}{dt} = \frac{- 2 αv}{(β + 2 αx)^{2}} = - 2 {αv}^{3}$

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