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\includegraphics[max width=\textwidth, alt={}, center]{102e108b-2a36-4765-9990-78e2dd4276c0-4_556_1373_269_386}
The diagram shows the ( \(t , v\) ) graph for the motion of a hoist used to deliver materials to different levels at a building site. The hoist moves vertically. The graph consists of straight line segments. In the first stage the hoist travels upwards from ground level for 25 s , coming to rest 8 m above ground level.
- Find the greatest speed reached by the hoist during this stage.
The second stage consists of a 40 s wait at the level reached during the first stage. In the third stage the hoist continues upwards until it comes to rest 40 m above ground level, arriving 135 s after leaving ground level. The hoist accelerates at \(0.02 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for the first 40 s of the third stage, reaching a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
- the value of \(V\),
- the length of time during the third stage for which the hoist is moving at constant speed,
- the deceleration of the hoist in the final part of the third stage.