A girl 
is riding a bicycle at a constant velocity of 
. At time 
, she passes a boy 
sitting on a bicycle that is stationary as illustrated by the diagram below.
At time , the boy sets off to catch up with the girl. He accelerates uniformly from time until he reaches a speed of 
in a time of 
. He then continues at a constant speed of . At time 
, the boy catches up with the girl.
is measured in seconds.
State, in terms of , the distance moved by the girl before the boy catches up with her.
For the boy, determine the distance moved during his acceleration.
For the boy, determine the distance moved during the time that he is moving at constant speed. Give your answer in terms of .
Use your answers in (a), (b) and (c) to determine the time taken for the boy to catch up with the girl.
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