A body starts from rest and travel 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:

A body starts from rest and travel distance S with uniform acceleratio

1.	A body starts from rest and travel 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:
Answer» Solution :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`