MW3 Investigate the relationship among distance, time, and speed for objects that undergo uniform motion

Suggested time: 5-7 hours

Learning Objectives

1. Collect data about everyday objects that undergo simple linear motion. (NUM)
   
2. Design an experiment and identify specific variables to be tested. (TL)
   
3. Develop appropriate sampling procedures for data collection in an experiment. (NUM)
   
4. Use appropriate instruments such as ticker timers, stopwatches, photogates, or motion detectors to collect data effectively and accurately.
   
5. Evaluate the relevance, reliability, and adequacy of data and data collection methods. (CCT)
   
6. Identify and explain sources of error and uncertainty in measurements.
   
7. Construct distance-time graphs to represent the uniform motion of everyday objects. (NUM)
   
8. Explain how the concept of rate of change relates to the concept of speed.
   
9. Operationally define distance and speed.
   
10. Define instantaneous speed and average speed as they relate to uniform motion.
    

Enrichment Learning Objectives

1. Express measured and calculated results in a form that acknowledges the degree of uncertainty. (NUM)
   
2. Distinguish among scalar and vector quantities, and the need for this distinction when studying simple linear motion.
   
3. Operationally define displacement and velocity.
   
4. Construct position-time graphs to represent the motion of everyday objects that undergo uniform motion.
   
5. Explain how the concept of rate of change relates to the concept of velocity.
   
6. Define instantaneous velocity and average velocity for uniform motion.
   

Key Questions

1. What is the relationship between distance, time, and speed for a moving object?
   
2. What are the differences between instantaneous and average motion measurements?
   
3. How can the motion of an object be represented graphically?
   
4. How does uniform motion appear on a distance-time graph?
   

Key Concepts

• Rate of change is a measure of how fast a quantity changes per unit time.
  
• Position is an object's location relative to a reference point.
  
• Distance is the length of path traveled between two points.
  
• Speed is the rate of change of distance of an object.
  
• Instantaneous speed refers to the actual speed of an object at a particular instant in time.
  
• Average speed refers to a calculation of change in distance over a time interval for a moving object.
  
• All measurements are subject to uncertainty based on the limits of the measuring device.
  
• Designing scientific experiments involves planning a series of data-gathering operations that will provide a basis for testing a hypothesis or answering a question.
  
• Variables are controlled in scientific experiments in order to determine the effect of changing one variable on another variable.
  
• Interpreting data is a process based on finding patterns in a collection of data that leads to generalizations.
  
• Scientific results are reproducible if all other conditions are identical.
  

Pre-Instructional Questions

1. Do students understand that "rate of change" denotes a change in some measurable quantity per unit of time?
   
2. Are the students able to identify equipment that they could use to make observations and collect data about the motion of everyday objects?
   
3. Are the students able to describe how they could collect data about moving objects?
   
4. Are the students able to use their prior observations of moving objects to generate testable questions about one or more aspects of motion?
   
5. Do the students understand the terms instantaneous and average ?
   

Suggested Teaching Strategies and Activities

1. Students should devise and perform experiments to collect data about objects that undergo uniform motion. Students should make decisions regarding: what object(s) to use for the experiment, what variables are to be tested, what variables are to be controlled, how to collect data, how much data to collect, how to organize the data, and how many trials to conduct. Students should graph their data on a distance-time graph in order to represent visually the relationship between object position and time variables. Students should save their graphs for quantitative analysis later in the unit. Many aspects of this activity can provide the foundation for further discussions of experimental methods. Students might write up their results using a narrative lab report rather than a formal lab report. (CCT, NUM)
   
   
2. Students should discuss methods of improving the relevance, reliability, and adequacy of data and data collection methods, and how different technologies might help resolve these issues. Some of the more common methods for collecting kinematics data in the classroom include: stopwatches and metre sticks, ticker tape timers, photogates, and motion detectors. Ticker tape timers have tended to be of great value in studying motion because students can obtain a large number of data points for an experiment of short duration. However, ticker tape timers are often not suitable outside of the classroom environment (e.g., student running on track, baseball in flight, moving vehicles). Students could also discuss that the motion being observed is not dependent on the technology used to measure that motion (i.e., collecting data using different technologies should result in similar representations of that motion). Students should recognize the positive effect technology can have on work and learning opportunities. (CD 6.3)
   
   
3. Students could discuss the challenges of collecting data on objects that are moving at very high (e.g., a plane flying) or very low speeds (e.g., an ant walking), situations for which ticker tape timers or metre sticks and stopwatches are not suitable. (CCT)
   
   
4. Students could use a video camera to collect data about moving objects, which enables students to analyze the motion frame by frame. The frames may be projected on a large screen for class analysis. Software is available specifically for analyzing video motion data that generates position-time data directly on the screen. (TL)
   
   
5. Students should identify examples of "rate of change" that are not motion-related and discuss how these rates might be similar to rate of change of distance or rate of change of position.
   
   
6. Students should describe examples from their own travel experiences to illustrate and explain the difference between instantaneous and average speed. Examples might include the speedometer readings of a car ride to school, the total time taken to drive to school, and the total distance traveled while driving to school.
   
   
7. Students could draw distance-time graphs to represent the motion of objects that students observe moving, without actually collecting data about those objects. For example, students could work in small groups to draw graphs of one other student moving forward and backward at constant or differing speeds. They can test their predictions by replicating the motion and collecting data using appropriate technologies. (CD 2.3)
   
   
8. Students could continue to link written and visual representations of motion by developing written descriptions of motion based solely on graphical representations of that motion (e.g., a distance-time graph). Conversely, students should be able to create an appropriate distance-time graph to represent a written description of motion.
   
   
9. Students could invite a police officer to discuss or demonstrate the use of a radar gun and other speed enforcement technologies such as aircraft. Some of these technologies report instantaneous values of speed, others report average values.
   
   
10. Students could compare various technologies that are used to determine the motion of objects. These technologies include RADAR, Laser, GPS, Doppler Radar, and infrared motion detectors. Students could explain how these technologies are able to determine the position or speed of objects.
    
    
11. Students could discuss the need for precision of motion-related measurements in different real world situations. Students should provide examples which require high precision (i.e., multiple decimal places) and examples in which answers can be less precise (i.e., rounded off to the nearest whole number).