1. © Nuffield Foundation 2012 Nuffield Free-Standing Mathematics Activity Modelling a test drive © Rudolf Stricker

2. © Nuffield Foundation 2010 Modelling a test drive The speed of the car measured accurately is not the same as that indicated by the speedometer.

3. © Nuffield Foundation 2010 Which speed is greater? Why do you think that could be? Is the difference always the same? Is there a rough rule to connect the two sets of speeds? How could you get a more accurate rule to link the two sets of data? Modelling a test drive Acceleration from rest Time t (seconds) True speed v (miles per hour) Indicated speed u (miles per hour) 2.33034 3.54045 5.05055 6.86066 9.47078 13.18089 20.59099

4. © Nuffield Foundation 2010 Modelling a test drive What can you say about the distance taken to stop after applying the brakes at different speeds? Why is it more difficult to know what sort of function will fit the data in this table? How could you try to find one? Brakes True speed v (miles per hour) Distance d (metres) 30 9.5 5027.5 7052.4 8598.7

5. At the end of the activity Which method of finding a model did you like best? Which method do you think is the most accurate? Would using a cubic or higher order function be better? If you found any part of the questions difficult, what could you do to improve your mathematical skills? © Nuffield Foundation 2012