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)ft_(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+`ft_(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)`
`thereforS=(ft^(2))/(72)`