# mathsbreaking

Extracts from this document...

Introduction

Mathematics

Course Work

Dominique Albert-Weiss

“Stopping disntances”

Table 1

Speed v (km/h) | Thinking distance (m) | Braking distance (m) |

32 | 6 | 6 |

48 | 9 | 14 |

64 | 12 | 24 |

80 | 15 | 38 |

96 | 18 | 55 |

112 | 21 | 75 |

- Use a GDC or graphing software to create two data plots: speed versus thinking distance and speed versus braking distance. Describe your results.

Graph 1

The given values in Table 1 of speed (km/h) and thinking distance (m) were plotted against each other in this graph. With close observation, it is noticeable that the speed is proportional to the thinking distance. In other words: the points construct a straight line that is going through the origin.

In this example, we are able to assume that the more the driver increases his/her speed, the more time it takes him/her to apply the brakes.

Graph 2

In graph 2, the values of Table 1 of speed (km/h)

Middle

y = 0.1875x

Function for graph 2 (speed vs. braking distance):

One way to find out the function of the graph to is by using the quadratic regression method.

This can only be done on the GDC (Graphic Calculator) and gives you the result:

y = 0.0061x² - 0.0232x + 0.6

- The overall stopping distance is obtained from adding the thinking distance to the braking distance. Create a data table of speed and overall stopping distance. Graph this data nad describe the results.

Total braking distance = thinking distance + braking distance

Table 2

Speed (km/h) | Thinking distance (m) | Braking distance (m) | Total braking distance (m) |

32 | 6 | 6 | 12 |

48 | 9 | 14 | 23 |

64 | 12 | 24 | 36 |

80 | 15 | 38 | 53 |

96 | 18 | 55 | 73 |

112 | 21 | 75 | 96 |

Graph 3

Therefore that the braking distance was added with the thinking distance, it is logical that the y-intercepts of graph 3 are higher than the ones of graph 1 and 2.

Conclusion

Table 3

Speed (km/h) | Stopping distance (m) |

10 | 2.5 |

40 | 17 |

90 | 65 |

160 | 180 |

Graph 4

Graph 4 represents the stopping distance and the time that were given in the table.

The function of speed vs. thinking distance which is y = 0.1875x, where x is equal the speed.

Speed (km/h) | Stopping distance (m) | Thinking distance (m) |

10 | 2.5 | 1.875 |

40 | 17 | 7.5 |

90 | 65 | 16.875 |

160 | 180 | 30 |

The same is done with the function of speed vs. braking distance which is y = 0.0061x² - 0.0232x + 0.6.

Speed (km/h) | Stopping distance (m) | Braking distance (m) |

10 | 2.5 | 0.978 |

40 | 17 | 9.432 |

90 | 65 | 47.922 |

160 | 180 | 153.048 |

It is shown that the results that were given at the beginning (thinking and braking distance) are both much lower than the results of the stopping distance.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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