Unit B: Changes in Motion

Lesson 1.4: Graphical Description of Uniform Motion


Imagine drinking a soft drink while riding in a vehicle that is moving along a straight, level road. The driver is keeping the speedometer at a constant speed—the vehicle is moving with uniform motion. With this kind of motion, you can hold a beverage so that the surface of the liquid remains level and appears motionless. If you are not travelling with uniform motion, watch out! You are more likely to spill your drink. A sudden stop—such as during a motor vehicle collision—will not only cause you to spill your drink, but may leave you with an injury.

Huge amounts of information can be communicated on graphs.  Graphs also help us see the patterns in the data.  This unit is about describing motion using three kinds of graphs.  By drawing and sketching graphs it is hoped that reading graphs will become a second nature skill.

  • Read pages 186 and 187 of the textbook. 

In the next investigation you will graph the motion of a toy bulldozer moving with uniform motion.   This type of activity helps many students better understand how motion can be represented in a graph, so it is strongly suggested that you do it.  Some assignment questions are based on this activity.
Read the investigation on pages 188 and 189 of the textbook.  If you wish, view the video on the right to better understand how a ticker tape timer works.  Follow the directions and answer the analysis questions.  Check your answers with those in the “Suggested Answers” .


  • Starting at “A Graph Tells a Story” on page 189 of the textbook, read up to the activity “Writing a Script to Describe Motion” on page 190.

The slope of a line of a position-time graph gives the speed of the object.  Work through the summary on page 192.
The area under a line of a velocity - time graph gives the displacement of an object.  Work through the summary on page 192.

You might like to try this little activity.  Open the Cat and Mouse gizmo.  Set the mouses head start to 10 m.  Set the mouses speed to 3.3 m/s and the cats speed to 6.6 m/s.  Run the Simulation.  Answer the questions below.

Any points chosen should give the same slopes.

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slope = 3.3 m/s


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mi»l«/mi»«mi»o«/mi»«mi»p«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mn»20«/mn»«mo»§#160;«/mo»«mi»m«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»m«/mi»«/mrow»«mrow»«mn»3«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»s«/mi»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»6«/mn»«mo».«/mo»«mn»6«/mn»«mo»§#160;«/mo»«mi»m«/mi»«mo»/«/mo»«mi»s«/mi»«/math»
The slope of a position time graph represents the speed.  Notice the units are m/s

Can you describe the motion represented by a position - time graph?  This activity might help you better understand how to describe motion.  Open the Distance-Time Graph Gizmo.  Set "number of points" to 5.  Set the points as shown in Figure 1.4a.  Describe the motion to yourself, then run the simulation to see if you were right.
Describe the motion as slow, fast or stationary, and forward and backward.
Play with the gizmo until you can consistently describe the motion.
Figure 1.4a

Is displacement equal to the area under the line?  
Figure 1.4b
Open the Distance - time and Velocity-time Graph gizmo.  Set it up as shown in figure 1.4b.  Describe the motion and run the simulation.  YOu can see that the displacement was zero.  look at the velocity-time graph and caluclate the displacement (remember there are positive and negative values of area)  The area should equal zero.
Set up motion that results in positive displacement.  See if the displacement is equal to the area under the graph.  



An object is accelerating for 10 seconds and then travelling at a constant velocity.  Note that you need only look at he the first 15 seconds.  The displacement is the area under the line.
total area = area of triangle + area of rectangle

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Figure 1.4c
This question represents the most challenging question of this type you may be given.

 

  • Read “1.4 Summary” on page 192 of the textbook. Then, complete “1.4 Questions” numbers 3 and 4 on page 193.  Check your answers in the “Practice Answers” .

Go to Assignment 1.4: Graphical Description of Uniform Motion.