A car, starting from rest, accelerates at the rate \( f \) through a distance \( S \), then cont...

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A car, starting from rest, accelerates at the rate \( f \) through a distance \( S \), then continues at constant speed for time \( t \) and then decelerates as the rate \( f / 2 \) to come to rest. If the total distance traveled is \( 15 \mathrm{~S} \), then:
a. \( S=f t \)
b. \( S=\frac{1}{6} f t^{2} \)
c. \( S=\frac{1}{72} f t^{2} \)
d. \( S=\frac{1}{144} f t^{2} \)
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