1.7.1: Problem Set
- Page ID
- 9470
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\ket}[1]{\left| #1 \right>}\)
\(\newcommand{\bra}[1]{\left< #1 \right|}\)
\(\newcommand{\braket}[2]{\left< #1 \vphantom{#2} \right| \left. #2 \vphantom{#1} \right>}\)
\(\newcommand{\braopket}[3]{\left< #1 \vphantom{#2}\vphantom{#3} \right| #2 \vphantom{#1}\vphantom{#3} \left| #3 \vphantom{#1}\vphantom{#2} \right>}\)
\(\newcommand{\qmvec}[1]{\mathbf{\vec{#1}}}\)
\(\newcommand{\op}[1]{\hat{\mathbf{#1}}}\)
\(\newcommand{\expect}[1]{\langle #1 \rangle}\)
\(\newcommand{\dfn}[1]{\emph{\textbf{#1}}}\)
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:
\(y=4.8 x^{2}+2 x+12\)