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 at the rate \( \frac{f}{2} \) to come to rest. If the total distance traversed is \( 15 \mathrm{~S} \), then [AIEEE 2005; AIIMS 2008]
(a) \( S=\frac{1}{2} f t^{2} \)
(b) \( S=\frac{1}{4} f t^{2} \)
(c) \( S=\frac{1}{72} f t^{2} \)
(d) \( S=\frac{1}{6} f t^{2} \)
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