A particle starts from rest and travels a distance L with uniform acceleration, then moves uniformly over a further distance 2L and finally came to rest after moving a further distance of 3L with unifom retardation. If the motion is rectilinear, then what is the ratio of average speed to maximum speed is

1. 1/5
2. 2/5
3. 3/5
4. 4/5

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A B C D

AB = L, BC = 2L, CD = 3L
it starts from rest and accelerates and then remains in uniform velocity and then retards
this means the maximum velocity will be at point B and let it be v
The velocity time graph is shown below



the area under velocity time graph is displacement and hence we have 3 equation corrosponding to regions AB, BC and CD



and the average velocity = tot.displacement/tot. time

and hence