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 $f/2$ to come to rest. If the total distance travelled is $15 \;S$, then :

Question

( A ) None of the above
( B ) $S = ft$
( C ) $S = \frac{1}{2} ft^2$
( D ) $S = \frac{1}{6} ft^2$