A body starts from rest and travels a distance `S` with uniform acceleration, then moves uniformly a distance `2S` uniformly , and finally comes to rest after moving further `5S` under uniform retardation. The ratio of the average velocity to maximum velocity is.

Explanation

area of `DeltaOAC S=(1)/(2)V_(max)t_(1)(or)t_(1)=(2S)/(V_(max))`,
area of `ABCD 2S=V_(max)t_(2)(or)t_(2)=(2S)/(V_(max))`
area of `DeltaBDE 5S=(1)/(2)V_(max)t_(3)(or)t_(3)=(10S)/(V_(max))`
`V_(avg)=("total displacement")/("total time")`
`V_(avg)=(S+2S+5S)/((2S)/(V_(max))+(2S)/(V_(max))+(10S)/(V_(max)))=(8S)/((14S)/(V_(max)))`
`(V_(avg))/(V_(max))=(8S)/(14S)=(4)/(7)`