Edexcel M1 2013 January — Question 5

Exam BoardEdexcel
ModuleM1 (Mechanics 1)
Year2013
SessionJanuary
TopicSUVAT & Travel Graphs

5.\(v \left( \mathrm {~m} \mathrm {~s} ^ { - 1 } \right) ^ { \wedge }\) Figure 4 The velocity-time graph in Figure 4 represents the journey of a train \(P\) travelling along a straight horizontal track between two stations which are 1.5 km apart.The train \(P\) leaves the first station,accelerating uniformly from rest for 300 m until it reaches a speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) .The train then maintains this speed for \(T\) seconds before decelerating uniformly at \(1.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) ,coming to rest at the next station.
(a)Find the acceleration of \(P\) during the first 300 m of its journey.
(b)Find the value of \(T\) . A second train \(Q\) completes the same journey in the same total time.The train leaves the first station,accelerating uniformly from rest until it reaches a speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and then immediately decelerates uniformly until it comes to rest at the next station.
(c)Sketch on the diagram above,a velocity-time graph which represents the journey of train \(Q\) .
(d)Find the value of \(V\) .