7. Two cyclists, Alice and Bobbie, travel from \(P\) to \(Q\) along a straight path. Alice starts from rest at \(P\) just as Bobbie passes her at \(3.5 \mathrm {~ms} ^ { - 1 }\). Bobbie continues at this speed while Alice accelerates at \(0.2 \mathrm {~ms} ^ { - 2 }\) for \(T\) seconds until she attains her maximum speed. At this moment both cyclists immediately start to slow down, with constant but different decelerations, and they come to rest at \(Q 80\) seconds after Alice started moving.

1. Sketch, on the same diagram, the velocity-time graphs for the two cyclists. By using the fact that both cyclists cover the same distance, find
2. the value of \(T\),
3. the distance between \(P\) and \(Q\),
4. the magnitude of Bobbie's deceleration.