SOLUTION: Modelling problem | My Assignment Tutor

Write a report of up to 2000 words on the modelling problem below. In no circumstances should your report exceed 3000 words; you may be penalised by up to 10 marks if it does. If a report obviously exceeds that limit, then your tutor will not mark any material beyond 3000 words. (These word limits may be taken as excluding the captions for diagrams or graphs, linking words between equations, and any appendices.) Your report should have the following section headings, which are based on the stages of the modelling cycle: Specify the purpose Create the model Do the mathematics Interpret the results Evaluate the model Revise the model Conclusions Modelling problem — Yellow lines When one is travelling by bus or car along a major road, one sometimes sees on the approach to a junction a succession of yellow lines painted across the carriageway. These warn the driver to slow down before reaching the junction. However, the lines are intended to do more than just warn: they are designed to encourage the driver to decelerate by creating the impression that the vehicle is going too fast otherwise. In order to do this, the lines are positioned progressively closer together as they get nearer to the junction. Crossing the lines provides a very strong visual clue to a vehicle’s speed (and also an auditory clue, as the lines are usually painted so as to produce a click as the vehicle passes over them). If a vehicle is approaching the junction at a constant speed, then the lines come past more and more quickly, giving the driver the feeling that the vehicle is accelerating. To compensate, the driver will tend to drive so that the lines come past at a constant rate. Thus drivers can be encouraged to slow down by careful spacing of the lines. Create a model for suggesting both the number and the spacing of the lines in order to take the greatest advantage of this effect.