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,

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