Print this chapterPrint this chapter

Lesson 6 Velocity vs. Speed

  Virtual Activity

Distance-Time and Velocity-Time Graphs © Explore Learning  https://moodle.adlc.ca/mod/lti/view.php?id=17251695


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

In this activity, you will work with a dynamic graph of the position of a runner over time, as well as a velocity-time graph and a distance traveled-time graph.

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.
  2. Check that the "Number of Points" is 2. Turn on "Show graph" and "Show animation" for both Runner 1 and Runner 2.

    Drag the endpoints on each line to create the graph shown in image C6.9.

    Runner 1’s line (the red one) should have endpoints at (0, 0) and (4, 40).

    Runner 2’s line (the blue one) should have endpoints at (0, 40) and (4, 20).
  3. Click the green button on the stopwatch to start the runners. Watch the two runners carefully. In what two ways are the runners’ motions different?

    The red runner (Runner 1) runs faster than the blue runner (Runner 2). Also, Runner 1 runs from left to right while Runner 2 runs from right to left.
    Activity A:
    Velocity-Time Graphs
    		Get the simulation ready:
    • Click the red button on the stopwatch to reset the runners..
    • Change the "Number of Points" to 5.
    • Turn off "Show graph" and "Show animation" for Runner 2.
    ©Explore Learning
    C6.10 appearance of graph

    Speed is a measure of how fast an object moves, regardless of direction. Speed can never be negative. Velocity describes both speed and direction, and can be positive or negative. For velocity, if it is negative, it means that object is moving in the reverse direction.

  4. In the simulation, make a position-time graph for Runner 1 with the following features:
    • There is at least one major change in speed.
    • There is at least one major change in direction.

    Click the green start button and watch the runner run. Adjust your graph if needed to meet the requirements.

    Sketch your graph.


    Note: Graphs will vary, but here is a sample one.
    ©Explore Learning
    C6.11 sample of graph


©Explore Learning
C6.9 Starting graph appearance
  1. Where was the runner each second? Based on your graph, fill in all except the final column in the table below. (Leave the velocity column blank for now.) Label any numbers with units.

    Note: Answers will vary. Sample answers below are based on sample graph above.

    Time Position at the End of the Time Interval (m) Distance Moved This Time Interval (m) To the left or right?
    		Velocity This Time Interval (m/s)
    0 to 1 sec 25 m
    		5 m
    		Right 5 m/s
    1 to 2 sec 0 m
    		25 m
    		Left –25 m/s
    2 to 3 sec 40 m
    		40 m
    		Right 40 m/s
    3 to 4 sec 25 m
    		15 m
    		Left –15 m/s

  2. To calculate the velocity for each time interval, first calculate the speed of the runner in that interval (speed = distance ÷ time). If the direction is left to right, velocity is positive. If the direction is right to left, velocity is negative. This is because the runner is moving in the reverse direction.

    Fill in the velocity column of the table above. Use units (m/s).

    When this runner is running to the left (negative velocity), what does his distance-time (position-time) graph look like?

    When running to the left, the runner’s position-time graph goes “downhill” from left to right. (It has a negative slope.)
  3. Slope is the steepness of a graph. To find the slope of a line, divide the change in y-value (rise) by the change in x-value (run). Like velocity, slope can be positive, zero, or negative.

    Fill in the slope of each segment of your position-time graph and the runner’s velocity during each time interval, in the table below.

    Note: Answers will vary. Sample answers below are based on sample graph above.

    Time Interval
    		Slope Velocity (m/s)
    0 sec to 1 sec
    		5 5 m/s
    1 sec to 2 sec
    		–25 –25 m/s
    2 sec to 3 sec
    		40 40 m/s
    3 sec to 4 sec
    		–15 –15 m/s

  4. Examine your velocities and the position-time graph you made. How is the slope of a position-time graph related to the velocity of the runner?

    The slope of a position-time graph is equal to the velocity of the runner.
  5. On the left side of the simulaion, select the "VELOCITY-TIME GRAPH" tab. Use the green probes to compare the velocity-time graph to the position-time graph.

    1. How does a velocity-time graph show that a runner is moving fast?

      A velocity-time graph has a y-value that is far from zero when the runner is running fast.
    2. How does a velocity-time graph show that a runner is moving from left to right?

      Moving from left to right is positive velocity, so a velocity-time graph has a positive difference between the y-values when the runner is moving left to right.
  1. Image 6.12 shows a position-time graph of a runner.

    First, sketch what you think his velocity-time graph will look like.

    Then check your answer in the simulation. You can do this by switching to the "VELOCITY-TIME GRAPH" tab.


    ©Explore Learning
    C6.13 velocity-time graph of a runner

    Activity B:
    Velocity and Position
    		Get the simulation ready:
    • Set the "Number of points" to 3.
    • Turn on "Show graph" and "Show animation" for both Runner 1 and Runner 2.
    ©Explore Learning
    C6.14 image of runners
©Explore Learning
C6.12 position-time graph of a runner

  1. In the simulation, make the position-time graphs shown in image C6.15.
    Click the green start button and watch the runners run. Sketch what you think their velocity-time graphs would look like. (If you can, use a red line for Runner 1, and a blue line for Runner 2.)

    Then select the "VELOCITY-TIME GRAPH" tab in the simulation. Sketch the actual graph.


    ©Explore Learning
    C6.16 velocity-time graph of two runners


  2. Make any position-time graphs you want for Runners 1 and 2. Sketch them. Then do the same thing as above: Sketch what you think their velocity-time graphs would look like, and then check.
©Explore Learning
C6.15 position-time graph of two runner
  1. Compare the velocity-time graphs to their related position-time graphs.

    1. When do two different position-time graphs have matching velocity-time graphs?

      This occurs when the position-time graphs have matching slopes.
    2. What information is missing from a velocity-time graph?

      Velocity-time graphs do not tell you anything about the runner’s position.
Activity C:
Distance and Displacement
Get the simulation ready:
  • Turn off "Show graph" and "Show animation" for Runner 2.
©Explore Learning
C6.17 image of runner

  1. Create the position-time graph for Runner 1 shown in image C6.18. Then fill in the blanks below to describe what you think the runner will do, based on that graph.

    The runner will run ___ metres in the first 2 seconds, with a velocity of ___ m/s.

    His direction will be from ___ to ___.

    Then he will run ___ metres in the next 2 seconds, with a velocity of ___ m/s.

    His direction will be from ___ to ___.

    The runner will run 40 metres in the first 2 seconds, with a velocity of 20 m/s.
    His direction will be from left to right.
    Then he will run 10 metres in the next 2 seconds, with a velocity of –5 m/s.
    His direction will be from right to left.
    Click the green start button and watch the runner go. Were you correct?
©Explore Learning
C6.18 position-time graph of a runner
  1. On top of the left half of the simulation, select the "DISTANCE TRAVELED" tab.
    1. What was the total distance travelled by the runner after 4 seconds?

      50 metres
    2. Displacement is equal to the difference between the starting and ending positions. Displacement to the right is positive while displacement to the left is negative. What is the displacement shown by the graph at the top of the page?

      30 metres
  2. In the simulation, create a position-time graph of a runner with these characteristics:
    • travels a distance of 60 metres in 4 seconds
    • has a displacement of +10 metres

    Sketch your graph.


    ©Explore Learning
    C6.19 position-time graph of a runner

  1. Look at the graph you made in step 16. Think about the speed of that runner.
    Answers below are based on graph above.

    1. What was the runner’s speed for the first 2 seconds?

      17.5 m/s
    2. What was the runner’s speed for the last 2 seconds?

      12.5 m/s
    3. What was the runner’s average speed over all 4 seconds?

  1. Now think about the velocity of the runner in question 4.
    Answers below are based on graph above.

    1. What was the runner’s velocity for the first 2 seconds?

      17.5 m/s
    2. What was the runner’s velocity for the last 2 seconds?

      –12.5 m/s
    3. What was the runner’s average velocity over all 4 seconds?

  2. Please return to the top of this page and click on analysis to complete the analysis questions.
  1. Suppose you knew the time, displacement, and total distance travelled by a runner.

    1. How would you calculate the runner’s average speed?

      Divide total distance travelled by time.
    2. How would you calculate the runner’s average velocity?

      Divide displacement by time.
  1. Image C6.20 is a graph of a runner. Calculate the values below for this runner. Include appropriate units.

    1. Distance travelled:

      100 m
       

    2. Displacement:


    3. Average speed:

      25 m/s
       

    4. Average velocity:

      5 m/s
       
C6.20 position-time graph of a runner


  Read This

Please read pages 142 and 476 to 477 in your Science 10 textbook. Make sure you take notes on your readings to study from later.  You should focus on how to calculate the slope of a position-time graph, and the information that can be interpreted from the slope of 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 the slope of a position-time graphs is useful in explaining an object’s motion.

    Your answer should be a variation of the following.
    The slope of a position-time graphs shows the velocity of a moving object. It can also show the direction the object is travelling.
  1. Use the graph in image C6.21 to answer the following questions.

    1. What is the velocity of the object from point A to point B?

      Point A: (0.0, 0)
      Point B: (60, 10)
      «math» «mi»s«/mi» «mi»l«/mi» «mi»o«/mi» «mi»p«/mi» «mi»e«/mi» «mo»=«/mo» «mfrac» «mrow» «mi»r«/mi» «mi»i«/mi» «mi»s«/mi» «mi»e«/mi» «/mrow» «mrow» «mi»r«/mi» «mi»u«/mi» «mi»n«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «msub» «mi»y«/mi» «mn»1«/mn» «/msub» «mo»-«/mo» «msub» «mi»y«/mi» «mn»2«/mn» «/msub» «/mrow» «mrow» «msub» «mi»x«/mi» «mn»1«/mn» «/msub» «mo»-«/mo» «msub» «mi»x«/mi» «mn»2«/mn» «/msub» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mn»0«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»-«/mo» «mn»60«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «mo»-«/mo» «mn»10«/mn» «mo»§#160;«/mo» «mi»s«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mo»-«/mo» «mn»60«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mo»-«/mo» «mn»10«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mo»+«/mo» «mn»6«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»/«/mo» «mi mathvariant=¨normal¨»s«/mi» «/math»

    2. What is the velocity of the object from point B to point C?

      The flat portion of the graph indicates the object is not moving. So, the velocity is zero.

    3. What is the velocity of the object from point C to point D?

      Point C: (60, 15)
      Point D: (–40, 40)
      «math» «mi»s«/mi» «mi»l«/mi» «mi»o«/mi» «mi»p«/mi» «mi»e«/mi» «mo»=«/mo» «mfrac» «mrow» «mi»r«/mi» «mi»i«/mi» «mi»s«/mi» «mi»e«/mi» «/mrow» «mrow» «mi»r«/mi» «mi»u«/mi» «mi»n«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «msub» «mi»y«/mi» «mn»1«/mn» «/msub» «mo»-«/mo» «msub» «mi»y«/mi» «mn»2«/mn» «/msub» «/mrow» «mrow» «msub» «mi»x«/mi» «mn»1«/mn» «/msub» «mo»-«/mo» «msub» «mi»x«/mi» «mn»2«/mn» «/msub» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mn»60«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»-«/mo» «mfenced» «mrow» «mo»-«/mo» «mn»40«/mn» «/mrow» «/mfenced» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mn»15«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «mo»-«/mo» «mn»40«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mn»100«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mo»-«/mo» «mn»25«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mo»-«/mo» «mn»4«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»/«/mo» «mi mathvariant=¨normal¨»s«/mi» «/math»


    4. What is the velocity of the object from point D to point E?

      Point D: (–40, 40)
      Point E: (0.0, 55)
      «math» «mi»s«/mi» «mi»l«/mi» «mi»o«/mi» «mi»p«/mi» «mi»e«/mi» «mo»=«/mo» «mfrac» «mrow» «mi»r«/mi» «mi»i«/mi» «mi»s«/mi» «mi»e«/mi» «/mrow» «mrow» «mi»r«/mi» «mi»u«/mi» «mi»n«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «msub» «mi»y«/mi» «mn»1«/mn» «/msub» «mo»-«/mo» «msub» «mi»y«/mi» «mn»2«/mn» «/msub» «/mrow» «mrow» «msub» «mi»x«/mi» «mn»1«/mn» «/msub» «mo»-«/mo» «msub» «mi»x«/mi» «mn»2«/mn» «/msub» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mn»0«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»-«/mo» «mfenced» «mrow» «mo»-«/mo» «mn»40«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «/mfenced» «/mrow» «mrow» «mn»55«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «mo»-«/mo» «mn»40«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mfrac» «mrow» «mn»40«/mn» «mo».«/mo» «mn»0«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «/mrow» «mrow» «mn»15«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»s«/mi» «/mrow» «/mfrac» «mo»=«/mo» «mo»+«/mo» «mn»2«/mn» «mo».«/mo» «mn»7«/mn» «mo»§#160;«/mo» «mi mathvariant=¨normal¨»m«/mi» «mo»/«/mo» «mi mathvariant=¨normal¨»s«/mi» «/math»
C6.21 Position-Time Graph