MW4 Investigate the relationship among speed, time, and acceleration for objects that undergo uniformly accelerated motion
Suggested time: 4-6 hours
The focus of this foundational objective is for students to increase their understanding of acceleration, using the context of everyday objects that undergo uniformly accelerated motion. Many students find the concept of acceleration difficult to understand because it is abstract, generally calculated rather than measured, and not easily observable like a change in position. Students should continue to develop expertise using written and graphical representations of motion.
Students should be reminded that few objects in the world undergo uniform acceleration for extended periods, thus the experiments and investigations in this section reflect simplified models of real-world behaviour.
Uniform acceleration can be positive or negative, which means that students can investigate objects that are speeding up at a constant rate as well as objects that are slowing down at a constant rate. Learning objectives related to quantitative analysis of uniformly accelerated motion appear in foundational objective MW5.
Learning Objectives
- Collect data about everyday objects that undergo uniformly accelerated motion. (NUM)
- Work collaboratively to plan and carry out investigations, as well as to generate and evaluate ideas to practice the skills, knowledge, and attitudes needed to work effectively with and for others. (PSD, CD 2.3)
- Construct and analyze distance-time and speed-time graphs of objects that undergo uniform acceleration. (NUM)
- Describe quantitatively the relationship among speed, time, and acceleration.
- Select and use appropriate vocabulary, units, symbols, and graphs to communicate information about moving objects. (COM)
- Value the role and contribution of science and technology in our understanding of phenomena that are directly observable and those that are not. (CD 6.3)
Enrichment Objectives
- Construct and analyze position-time and velocity-time graphs of objects that undergo uniform acceleration.
- Describe quantitatively the relationship among velocity, time, and acceleration.
Key Questions
- What is acceleration?
- How are speed, time, and acceleration related?
- How can uniformly accelerated motion be represented graphically?
Key Concepts
- Acceleration is the rate of change of an object's speed, which may be a change in magnitude of the speed or a change of direction of the speed. (The former is a topic of study in this unit; the latter is not.)
- The acceleration of an object may be in a direction that is different from the direction of its motion.
- Models (physical, mathematical, or conceptual) are simplified representations of real phenomena that facilitate a better understanding of some scientific concepts or principles.
- Hypothesizing is stating a tentative generalization that may explain a large number of events and that may be tested experimentally.
Pre-Instructional Questions
- What is the students' understanding of the term acceleration?
- Are students able to recognize or give examples of objects that are accelerating?
- Are students able to suggest how they might gather data to determine whether an object is accelerating?
Suggested Teaching Strategies and Activities
- Students should predict the shape of distance-time graphs and speed-time graphs for objects that undergo uniformly accelerated motion (e.g., ball rolling down a ramp, ball with an initial velocity rolling up a ramp, object falling), and then conduct an experiment to gather data that will support or refute their predictions.
- Students should devise and carry out experiments to collect data about objects that undergo uniformly accelerated 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. Although the classic physics experiment for this concept involves a dynamics cart rolling down an inclined plane, students should be encouraged to consider other experimental designs. Students should represent their data using both speed-time and distance-time graphs. Students might complete a formal lab report for these experiments. (COM, NUM)
- Students could replicate Galileo's classic experiment of "diluting" the acceleration of an object in order to be able to measure that acceleration.
Galileo realized that most objects in free fall fell too fast for accurate position and time data collection in his time, which was before stopwatches and photogates. His experiment consisted of a round bronze ball placed in a straight, smooth, and polished groove within a piece of wooden moulding 12 cubits long, all of which was set upon an inclined plane. Galileo "diluted" the acceleration by adjusting the angle of the inclined plane so that his measuring device, a water clock, could be used to collect data. Students might choose to build a replica of the water clock or devise their own similar time keeping device.
- Students could build a balloon, mousetrap, or elastic band powered vehicle and collect data about the object while it is accelerating and then while it is decelerating. Students could graph these motions to determine the uniformity of the object's acceleration and deceleration.
- Students could discuss the role of technology in attaining information about acceleration (CD 6.3). Although our bodies can "feel" changes in speed (of sufficiently high positive or negative values) in instances such as amusement park rides, elevators, or automobiles, we are generally unable to determine the magnitude of the changes in speed. For example, does an elevator traveling from the main to third floor of a building accelerate at the same rate as an elevator traveling from the main to the tenth floor of a building? Students should discuss different technologies that can detect and measure acceleration.