5.3: Trains in Motion
This activity is intended to supplement Algebra I, Chapter 4, Section 8.
ID: 11194
Time required: 15 minutes
Activity Overview
In this activity, students will make observations about the motion of two objects. They will compare and contrast this motion and consider how it corresponds to a graph representing distance as a function of time. As an extension, students will explore the relationship between the slope and the rate.
Topic: Linear Equations & Functions

Motion, distance = rate \begin{align*}\cdot\end{align*}
⋅ time  Slope, graphically expressing data
Teacher Preparation and Notes
 This activity can serve as a nice introduction to using formulas and graphs to represent a reallife situation.
 The student worksheet provides instructions and questions to guide the inquiry and focus the observations.
 Be sure to add the program to each student’s graphing calculator.
 To download the TRAINS program go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=11194 and select "TRAINS.8xp" to download.
Associated Materials
 Student Worksheet: Trains in Motion, http://www.ck12.org/flexr/chapter/9614, scroll down to the third activity.
 TRAINS (program)
In this activity, students use the program TRAINS to view two graphs. Make sure that students have loaded the program before beginning the activity. The first graph is of two trains leaving a train station. The second is the distancetime graph of this motion.
Problem 1 – Observe Motion
After selecting the first option of the program OBSERVE MOTION, students will see two lines and a circle that travels each line. The circle represents the trains. Explain to students that even though the lines (tracks) stop, in the real world the train tracks would continue on. Also, students should pretend that there is track connecting the first train to the station.
When students press TRACE, three values will appear at the bottom of the screen. The \begin{align*}T\end{align*}
Students can press \begin{align*}2^{nd}\end{align*}
Answers to the worksheet questions.
1. Answers will vary, but the following question should complement their answers.
2. When \begin{align*}t = 0\end{align*}
3. Train \begin{align*}2\end{align*}
4. Train \begin{align*}2\end{align*}
5. Train \begin{align*}2\end{align*}
6. Train \begin{align*}1\end{align*}
7. Train \begin{align*}1\end{align*}
8. They are at the same distance from the station at \begin{align*}240 \ km\end{align*}
9. This occurs at \begin{align*}2 \ hours\end{align*}
Problem 2 – DistanceTime Graph
After selecting the second option of the program DIST VS TIME, students will see two lines will positive slopes, which intersect each other.
When students press TRACE, two values will appear at the bottom of the screen. The \begin{align*}X\end{align*}
Students should understand that the intersection point of the two lines is the time at which the trains are equal distance from the station.
Pressing \begin{align*}2^{nd}\end{align*}
Answers to the worksheet questions.
10. Train 2 has a steeper slope.
11. The slope is the speed or rate of change of distance.
12. a) \begin{align*}y\end{align*}
b) \begin{align*}y\end{align*}
13. This indicates their starting location.
14. train \begin{align*}1:d = 80t + 80\end{align*}
Also acceptable would be \begin{align*}y = 80x + 80\end{align*}
15. \begin{align*}80t + 80 = 120t \rightarrow 80 = 40t \rightarrow t = 2 \ hr\end{align*}
Extension: Problem 2 – List of \begin{align*}d = r \cdot t\end{align*}
This extension introduces a numeric and graphical exploration. Students begin by determining what the next time and distance values would be in the list.
16. \begin{align*}5 \ hr\end{align*}
Students then are instructed to go to the data lists and change the data depending upon a different \begin{align*}r\end{align*}
17. When \begin{align*}r\end{align*}
When \begin{align*}r\end{align*}
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