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 [AIEEE 2005]

• 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.                                  \[S=\frac{1}{6}f{{t}^{2}}\]