A car starting from rest, accelerates at the rate of f through a distance S, then continues at constant speed for time t and declerates at the rate f/2 to come to rest. If the total distance travelled is 15 S then S =

Explanation

`AB=S=1/2 f t_(1)^(2) …………(1)`
`v=ft_(1)`
`BC=vt=(ft_(1))t …….(2)`
`CD=u^(2)/(2a)=((ft_(1))^(2))/(2(f//2))=2S…….(3)`
`S+f t_(1) t+2S=15S`
`ft_(1) t=12S……..(4)`
Dividing (4) by (1) `t_(1)=t/6`
Now (1) gives `S=1/2 f t^(2)/(36)`
`S=(ft^2)/(72)`