Position-Time Graphs

What can a position-time graph tell us about an object’s motion?


C5.15 runner on running track
Sometimes in science, you are asked to plot data on a graph yourself, and sometimes a graph is provided to you. Either way, a graph can tell us a lot about an object’s motion. Distance-time graphs, also known as position-time graphs, can be used to interpret the direction an object is travelling, whether it is moving or stationary, and the distance travelled over a specific time period.

  Virtual Activity


Distance-Time Graphs © Explore Learning

Work through this activity to discover how the motion of a runner can be plotted on a distance-time graph. You will learn what information can be interpreted from the shape of the line on a distance-time graph.

The activity shows a graph and a runner on a track. You can control the motion of the runner by manipulating the graph (drag the red dots).

Please note: if you scroll down while in the Gizmo you will see a list of questions. You DO NOT need to complete these questions. You are able to complete them for extra practice if you would like.

  1. Click on the play button to open the activity. This activity can also be accessed in the Online Resources for Print Students section of your online course.
  1. Check that "Number of points" is 2, and that under "Runner 1" both "Show graph" and "Show animation" are turned on.

    The graph should look like the one shown in image C5.16 – one point at (0, 0) and the other point at (4, 40).
  1. Click the green button stopwatch to start the runner. What happens?

    The runner runs from left to right for 4 seconds, stopping at the 40-metre line.
  2. Click the red button on the stopwatch to reset the runner. The vertical green probe on the graph allows you to see a snapshot of the runner at any point in time. Drag it back and forth. As you do, watch the runner and the stopwatch.

    1. What was the position of the runner at 1 second?

      10 metres
    2. What are the coordinates of the point on the graph that tells you this?

    3. When was the runner on the 30-metre line?

      At 3 seconds
    4. What are the coordinates of the point on the graph that tells you this?

    3. Part A:
    Runner Position
    		Get the simulation ready:
    • Click the red button on the stopwatch to reset the runner.
    • Be sure the "Number of points" is 2.
    ©Explore Learning
    C5.17 appearance of runner position

©Explore Learning
C5.16 Starting graph appearance
In the simulation, run the “race” many times with a variety of different graphs. To run the race you must click on the green button on the stop watch. (You can change the graph by dragging the two red points on the graph up and down). Pay attention to what the graph tells you about the runner.

  1. If a distance-time graph contains the point (4, 15), what does that tell you about the runner? (Be specific, and answer in a complete sentence.)

    This tells you that after 4 seconds of running, the runner was 15 metres from the starting line.
  2. Look at the graph in image C5.18. Notice where the green probe is. If you could see the runner and the stopwatch at this moment, what would you see?

    The runner would be on the 20-metre line, facing left. The stopwatch would read approximately 1.5 seconds (or 1:50).
©Explore Learning
C5.18 green probe position
  1. Look at image C5.19, from the simulation. What must be true about this runner’s graph?


    ©Explore Learning
    C5.19 runner at 3.25 s


    The graph of the runner must include the point (3.25, 25). Also, the graph has a positive, or “uphill,” slope at that point. This is because the runner is facing forward in the image, so he must be running from left to right.

    If the runner had been running from right to left, the graph would have a negative, or “downhill,” slope at that point.
  1. The point on the graph that lies on the y-axis (vertical axis) is called the y-intercept. What does the y-intercept tell you about the runner?

    The y-intercept indicates the starting position of the runner.
  2.  In the simulation, set the "Number of points" to 3. Then create a graph of a runner who starts at the 20-metre line, runs to the 40-metre line, and finishes at the 30-metre line.

    1. Sketch what your graph would look like.


      ©Explore Learning
      C5.20 graph of a runner with described points


    2. What is the y-intercept of your graph?

      (0, 20) or 20 m
      Part B:
      Runner direction and speed
      		Get the simulation ready:
      • Click the red reset button on the simulation and make sure you have three points still selected.
      ©Explore Learning
      C5.21 appearance of graph

      Run the simulation several times with different types of graphs. (Remember, the red points on the graph can be dragged vertically.) Pay attention to the speed and direction of the runner.

  1. Create a graph of a runner that is running forward (from left to right) in the simulation.

    1. Sketch what your graph would look like.

      There are several possible correct answers. This is an example:


      ©Explore Learning
      C5.22 graph of a runner with described motion


    2. If the runner is moving from left to right in the simulation, how will the graph always look?

      The graph will have a positive slope. (The line will go from the lower left to the upper right.)
  1. Click the red reset button. Create a graph of a runner that is running from right to left.

    1. Sketch what your graph would look like.

      There are several possible correct answers. This is an example:


      ©Explore Learning
      C5.23 graph of a runner with described motion


    2. How does the graph always look if the runner is moving from right to left in the simulation?

      The graph will have a negative slope. (The line will go from upper left to lower right.)
  1. Change the "Number of points" to 5. Create a graph of a runner that runs left-to-right for 1 second, rests for 2 seconds, and then continues running in the same direction.

    1. Sketch what your graph would look like.

      There are several possible correct answers. This is an example:


      ©Explore Learning
      C5.24 graph of a runner with described motion


    2. How does a graph show a runner at rest?

      The line will be horizontal when the runner is at rest.

  1. With "Number of points" set to 3, create the graph in image C5.25.
    Your graph should include (0, 0), (2, 10), and (4, 40).

    1. Where does the runner start?

      0-metre line
    2. Where will he be after 2 seconds?

      10-metre line
    3. Where will he be after 4 seconds?

      40-metre line
    4. In which time interval do you think the runner will be moving most quickly?

      2 to 4 seconds

©Explore Learning
C5.25 number of points set to 3
  1. Click the green start button and watch the animation. What changed about the runner after 2 seconds of running?

    The speed of the runner increased.
  2. Speed is a measure of how fast something is moving. To calculate speed, divide the distance by the time. In the simulation, the units of speed is metres per second (m/s).

    1. In the first 2 seconds, how far did the runner go?

      10 metres
    2. In this time interval, how far did the runner go each second?

      5 metres
    3. In this time interval, what was the runner’s speed?

      «math» «mi»v«/mi» «mo»=«/mo» «mfrac» «mrow» «mo»§#8710;«/mo» «mi»d«/mi» «/mrow» «mrow» «mo»§#8710;«/mo» «mi»t«/mi» «/mrow» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «mi»v«/mi» «mo»=«/mo» «mfrac» «mrow» «mn»30«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mn»2«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «/math»

      5 metres/second (5 m/s)
  1. Now look at the last 2 seconds represented on the graph.

    1. In the last 2 seconds, how far did the runner go?

      30 metres
    2. In this time interval, how far did the runner go each second?

      15 metres
    3. In this time interval, what was the runner’s speed?

      «math» «mi»v«/mi» «mo»=«/mo» «mfrac» «mrow» «mo»§#8710;«/mo» «mi»d«/mi» «/mrow» «mrow» «mo»§#8710;«/mo» «mi»t«/mi» «/mrow» «/mfrac» «mspace linebreak=¨newline¨»«/mspace» «mi»v«/mi» «mo»=«/mo» «mfrac» «mrow» «mn»30«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mn»2«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «/math»

      15 metres/second (15 m/s)
  2. Please return to the top of this page and click on analysis to complete the analysis questions.

  Did you know?

C5.26 Canada goose

Canada geese migrate in order to return to the area where they were born for mating and nesting.

Not all Canada geese migrate, but many do who make their summer homes in Canada do migrate.

Migrations can be as long as 3 200 km to 4 800 km, and the geese are capable of flying up to 2 400 km in a single day if the weather is good.

This measurement is distance flown by the geese, not displacement. The geese do not fly in a directly straight path.
  1. In general, how does a distance-time graph show you which direction the runner is moving?

    The runner’s direction is given by the slope of the graph. A positive slope ( / ) indicates the runner is moving forward, or from left to right. A negative slope ( \ ) indicates the runner is moving backward, or from right to left.

  2. How can you estimate the speed of the runner by looking at a graph?

    The steeper the line on the graph, the faster the runner.

  Read This

Please read pages 137 to 138, and 142 in your Science 10 textbook. Make sure you take notes on your readings to study from later. You should focus on how to create a position-time graph, and the information that can be interpreted from a position-time (distance-time) graph. Remember, if you have any questions, or do not understand something, ask your teacher!

  Practice Questions

Complete the following practice questions to check your understanding of the concept you just learned. Make sure you write complete answers to the practice questions in your notes. After you have checked your answers, make corrections to your responses (where necessary) to study from.

  1. Explain how distance-time graphs are useful in explaining an object’s motion.

    Your answer should be a variation of the following.
    Distance-time graphs show the starting position, direction, and speed of a moving object.
  2. Use the graph in image C5.27 to answer the following questions.

    C5.27 Position-Time Graph



    1. Describe the motion of the object from point A to point B.

      A positive slope indicates the object is moving forward.
    2. Describe the motion of the object from point B to point C.

      The flat portion of the graph indicates the object is not moving.
    3. Describe the motion of the object from point C to point D.

      A negative slope indicates the object is moving backward.
    4. What is the total distance travelled by the object?

      Read from the graph that point A is at 1 m and point B is at 3 m. The distance from point A to point B is 2 m.
      Read from the graph that point B is at 3 m and point C is at 3 m. The distance from point B to point C is 0 m.
      Read from the graph that point C is at 3 m and point D is at 0 m. The distance from point C to point D is 3 m.
      To calculate the distance, you would perform the calculation Δd = 2.0 m + 0.0 m + 3.0 m = 5.0 m.
    5. What is the total displacement of the object?

      To calculate the displacement, you would add the three values, taking into account that positive slope is a positive direction and negative slope is a negative direction.

      «math» «mi»§#916;«/mi» «mover» «mi»d«/mi» «mo»§#8594;«/mo» «/mover» «mo»=«/mo» «mo»(«/mo» «mo»+«/mo» «mn»2«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»)«/mo» «mo»+«/mo» «mo»(«/mo» «mn»0«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»)«/mo» «mo»+«/mo» «mo»(«/mo» «mo»§#8211;«/mo» «mn»3«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»)«/mo» «mo»§#160;«/mo» «mo»=«/mo» «mo»§#8211;«/mo» «mn»1«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/math»
       
      Because negative slope is negative, then an answer of –1.0 m means that you could express it as «math» «mo»§#160;«/mo» «mi»§#916;«/mi» «mover» «mi»d«/mi» «mo»§#8594;«/mo» «/mover» «mo»=«/mo» «mo»-«/mo» «mn»1«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»§#160;«/mo» «mi»or«/mi» «mo»§#160;«/mo» «mn»1«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»§#160;«/mo» «mo»[«/mo» «mi»backward«/mi» «mo»]«/mo» «mo».«/mo» «/math»