A body starts from rest and travels a distance S with uniform acceleration, then moves uniformly a distance 2S and finally comes to rest after moving further 5S under uniform retardation. Find the ratio 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) ot t_(2)=(2S)/(V_("max"))`
`5S=1/2 V_("max") t_(3) or t_(3)=(10S)/(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 (OR)`
`(V_(av))/V_("max")=("Total displacement")/(2("total displacement during acceleration andretardaton")+("Displacement During uniform velocity"))`
`V_(av)/(V_("max"))=(8S)/(2(S+5S)+2S)=(8)/(14)=(4)/7`