1.7.1: Problem Set

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

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.

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.

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:

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