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) therefore S=(ft^(2))/(72)`