A particle starts from rest and travels a distance s with uniform acceleration, then it travels a distance 2s with uniform speed, finally it travels a distance 3s with uniform retardation and comes to rest. If the complete motion of the particle in a straight line then the ratio of its average velocity to maximum velocity in

When a particle is moving with uniform acceleration, let b the velocity of particle at a distance s, 

Then average velocity  $=\frac{0+v}{2}=\frac{v}{2}$

Time taken, $t_1=\frac{s}{(v/2)}=\frac{2s}{v}$

When particle moves with uniform velocity, time taken, 

$t_2=\frac{2s}{v}$

When particle moves with uniform acceleration, time taken, 

$t_3=\frac{3s}{(0+v)/2}=\frac{6s}{v}$

Total time $=t_1+t_2+t_3$

$=\frac{2s}{v}+\frac{2s}{v}+\frac{6s}{v}=\frac{10s}{v}$

$\therefore v_{av}=\frac{s+2s+3s}{10s/v}=\frac{6v}{10}$

or $\frac{v_{av}}{v}=\frac{6}{10}=\frac{3}{5}$