16.7: Polynomial Fitting Problem Set

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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.

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

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.

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:

$$y=4.8 x^{2}+2 x+12$$

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)

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