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The velocity of a particle moving in a straight line at time 
seconds after leaving a fixed point O is 
. The diagram shows a velocity-time graph which models the motion of the particle from 
to 
. The graph consists of four straight line segments. The particle accelerates from rest to a speed of 
over a period of 
, and then decelerates at 
to instantaneous rest over a period of 
. The particle then travels back towards O, reaching a maximum speed of 
before coming to rest at time . Find the value of 
.
