Angular displacement θ of a flywheel varies with time as θ=at+b

Question

Angular displacement

θ

of a flywheel varies with time as

θ = a t + b t^{2} + c t^{3}

, then angular acceleration of the flywheel is given by

Options:

A . a+2bt−3ct2

B . 2b−6t

C . a+2b−6t

D . 2b+6ct

Answer: Option D
:
D
Angular acceleration

α = \frac{d^{2} θ}{d t^{2}} = \frac{d^{2}}{d t^{2}} (a t + b t^{2} + c t^{3}) = 2 b + 6 c t

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