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. The ratio of the average velocity to maximum velocity is

Graphically, the area of v-t curve represents displacement: S=12vmaxt1  or  t1=2Svmax2S=vmaxt2      or  t2=2Svmax5S=12vmaxt3  or  t3=10Svmaxvav = Total displacement  Total time =S+2S+5S2Svmax+2Svmax+10Svmaxvavvmax=8S14S=47.Alternative: vavvmax= Total displacement 2 Total displacement  during acceleration  and retardation + Displacement  during uniform  velocity vavvmax=8S2(S+5S)+2S=814=47