A motor powers a model car so that after starting from rest, the car travels \(s\) feet in \(t\) seconds, where \(s=12t\sqrt{t}\). Which of the following gives the average speed of the car, in feet, per second, over the first \(t\) seconds after it starts?

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The average speed of a car can be derived from the standard rate equation:

$$ d=rt $$ $$ r=\frac{d}{t} $$

We are told that the distance traveled is \(12t\sqrt{t}\). Therefore,

$$ r=\frac{12t\sqrt{t}}{t} $$ $$ r=\boxed{12\sqrt{t}} $$