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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 at the rate \( \frac{f}{2} \) to come to rest. If the total distance traversed is \( 15 S \), then
(1) \( S=\frac{1}{2} f t^{2} \)
(2) \( S=\frac{1}{4} f t^{2} \)
(3) \( S=\frac{1}{72} f t^{2} \)
(4) \( S=\frac{1}{6} f t^{2} \)
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