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