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A car, starting from rest, accelerates at the rate \( f \) through a distance \( \mathrm{S} \), then continues at constant speed for time
\( P \) t and then decelerates at the rate \( \frac{f}{2} \) to come to rest. If

W the total distance traversed is \( 15 \mathrm{~S} \), then
(1) \( \mathrm{S}=\frac{1}{2} f t^{2} \)
(2) \( \mathrm{S}=\frac{1}{4} f t^{2} \)
(3) \( \mathrm{S}=\frac{1}{72} f t^{2} \)
(4) \( \mathrm{S}=\frac{1}{6} f t^{2} \)
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