CAIE M1 2005 June — Question 6

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2005
SessionJune
TopicSUVAT & Travel Graphs

6
\includegraphics[max width=\textwidth, alt={}, center]{9bb53600-e7ba-4228-84ae-d8ddf7649387-3_735_1484_625_333} The diagram shows the velocity-time graph for a lift moving between floors in a building. The graph consists of straight line segments. In the first stage the lift travels downwards from the ground floor for 5 s , coming to rest at the basement after travelling 10 m .
  1. Find the greatest speed reached during this stage. The second stage consists of a 10 s wait at the basement. In the third stage, the lift travels upwards until it comes to rest at a floor 34.5 m above the basement, arriving 24.5 s after the start of the first stage. The lift accelerates at \(2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for the first 3 s of the third stage, reaching a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
  2. the value of \(V\),
  3. the time during the third stage for which the lift is moving at constant speed,
  4. the deceleration of the lift in the final part of the third stage.