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

Step-by-step solution

Graphically, the area of v-t curve represents displacement: S= 1 2 v_ t₁ or t₁= 2 S v_ 2 S=v_ t₂ or t₂= 2 S v_ 5 S= 1 2 v_ t₃ or t₃= 10 S v_ aligned v_ av & = Total displacement Total time & = S+2 S+5 S 2 S v_ max + 2 S v_ + 10 S v_ v_ av v_ max & = 8 S 14 S = 4 7 aligned