OCR M1 2007 January — Question 6

Exam BoardOCR
ModuleM1 (Mechanics 1)
Year2007
SessionJanuary
TopicSUVAT in 2D & Gravity

6
\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.
  1. 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
  2. the value of \(V\),
  3. the length of time during the third stage for which the hoist is moving at constant speed,
  4. the deceleration of the hoist in the final part of the third stage.