# 10.2 Problem Set

- Page ID
- 9470

Using the following experimental values ^{1}, plot a distance-time graph and determine the equation, relating the distance and time for a moving object.

Distance [m] |
Time [s] |

0 | 0 |

24 | 5 |

48 | 10 |

72 | 15 |

96 | 20 |

Experimental data.

**Answer:**-
Data can be entered as follows: distance=[0 24 48 72 96]; time=[0 5 10 15 20]; we can now plot the data by typing in plot(time,distance);title('Distance-Time Graph');xlabel('time');ylabel('distance'); at the MATLAB prompt. The following plot is generated, select Tools > Basic Fitting:

As shown above, the relationship between distance and time is:

\(y=4.8 x-1.7 \times 10^{-14}\)

or

Distance \(=4.8\) Time \(-1.7 \times 10^{-14}\)

Using the data set below, determine the relationship between temperature and internal energy.

Temperature [C] |
Internal Energy [kJ/kg] |

100 | 2506.7 |

150 | 2582.8 |

200 | 2658.1 |

250 | 2733.7 |

300 | 2810.4 |

400 | 2967.9 |

500 | 3131.6 |

An extract from Steam Tables

**Answer:**-
Data can be entered as follows:temperature = [100, 150, 200, 250, 300, 400, 500]; energy = [2506.7, 2582.8, 2658.1, 2733.7, 2810.4, 2967.9, 3131.6]; we can now plot the data by typing in plot(temperature,energy);title('temperature vs. energy');xlabel('temperature');ylabel('energy'); at the MATLAB prompt. The following plot is generated, select Tools > Basic Fitting:

As shown above, the relationship between temperature and internal energy is:

\(y=1.6 x+2347.2\)

or

internal energy \(=1.6\) temperature \(+2347.2\)

Using the following experimental values ^{2}, plot a velocity-time graph and determine the equation, relating the velocity and time for a moving object.

Velocity [m/s] |
Time [s] |

12 | 0 |

142 | 5 |

512 | 10 |

1122 | 15 |

1972 | 20 |

Experimental data.

**Answer:**-
Data can be entered as follows: velocity=[12 142 512 1122 1972]; time=[0 5 10 15 20]; we can now plot the data by typing in plot(time,velocity);title('Velocity-Time Graph');xlabel('time');ylabel('velocity'); at the MATLAB prompt. The following plot is generated, select Tools > Basic Fitting, notice that we are choosing the quadratic option this time:

As shown above, the relationship between velocity and time is:

\(y=4.8 x^{2}+2 x+12\)