A current through a wire depends on time as \( i=\alpha_{0} t+\beta t^{2} \) where \( \alpha_{0}...

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A current through a wire depends on time as \( i=\alpha_{0} t+\beta t^{2} \) where \( \alpha_{0}=20 \mathrm{~A} / \mathrm{s} \) and \( \beta=8 \mathrm{~A} \mathrm{~s}^{-2} \). Find the charge crossed through a section of the wire in \( 15 \mathrm{~s} \).
(a) \( 2100 \mathrm{C} \)
(b) \( 260 \mathrm{C} \)
(c) \( 2250 \mathrm{C} \)
(d) \( 11250 \mathrm{C} \)
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