## anonymous one year ago given that time t =ax^2 +bx, where a and b are constants. show that the retardation is 2av^3 where v is the instantaneous velocity.

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1. IrishBoy123

$$t =ax^2 +bx$$ $$\frac{dt}{dx} = 2ax + b$$ [or $$1 = 2ax \frac{dx}{dt} + b \frac{dx}{dt} = \frac{dx}{dt} (2ax+b)$$ etc] $$\frac{dx}{dt} = \frac{1}{2ax + b} [= v]$$ $$\frac{d^2x}{dt^2} = \frac{-2a}{(2ax + b)^2} [= -2av^2]$$ not $$v^3$$