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

Explanation

Graphically:Area of (V-t)curve represent displacement

`S=(1)/(2)V_(max)t_(1)` or `t_(1)=(2S)/(V_(max))`,
2S=`V_(max)t_(2)` or `t_(2)=(2S)/(V_(max))`
`V_(av)=("Total displacement")/("Total time"),V_(av)=(S+2S+5S)/((2S)/(V_(max)+(2S)/(V_(max))+(10S)/(V_(max))))`
`(V_(av))/(V_(max))=(8S)/(14S)=(4)/(7)`
`(V_(av))/(V_(max))=("Total displacement")/(2("total displacement during acceleration andretardaton")+("Displacement During uniform velocity"))`
`therefore (V_(av))/(V_(max))=(8S)/(2(S+5S)+2S)=(8)/(14)=(4)/(7)`