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Engineering LibreTexts

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:

    屏幕快照 2019-05-28 19.10.41.png

    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:

    屏幕快照 2019-05-28 19.16.26.png

    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:

    屏幕快照 2019-05-28 19.20.33.png

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

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

    Footnotes

    • 1 Engineering Science by E. Hughes and C. Hughes, Longman © 1994, (p. 375)
    • 2 Engineering Science by E. Hughes and C. Hughes, Longman © 1994, (p. 375)