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 traversed is `15 S` , then

Explanation

for time `t_(1) v_(m)=ft_(1)` and `S=(1)/(2)ft_(1)^(2)`
for time `t_(3)0=v_(m)-(f)/(2)t^(2)rArrt_(2)=2t_(1)`
`S_(3)=(1)/(2)((f)/(2))t_(2)^(2)=((f)/(4))(4t_(1)^(2))=ft_(1)^(2)=2S`
Therefore `S+v_(m)t+2S=15SrArrv_(m)t=12SrArrft_(1)t=12S`
`rArrf((2S)/(f))^(1//2)t=12S rArr 2Sf=(144S^(2))/(t^(2))rArrS=(ft^(2))/(72)`