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Learning Introductory Physics with Activities

Section 2.12 Challenge - Motion

Subsubsection Explanation Tasks

If necessary, review the Explanation Task Steps.

Explanation 2.12.1. Moving Cars.

At \(t_1\text{,}\) car A and car B are each located at position \(x_o\) moving forward at speed \(v\text{.}\) At \(t_2\text{,}\) car A is located at position \(2x_o\) moving forward at speed \(3v\text{,}\) while car B is located at position \(2x_o\) but is moving backward at speed \(v\text{.}\)
Is the average velocity of car A between \(t_1\) and \(t_2\) greater than, less than, or equal to the average velocity of car B between \(t_1\) and \(t_2\text{?}\)

Explanation 2.12.2. Bouncing Bumper Cars.

Two bumper cars roll toward each other as shown in the figure below. The left side shows the cars before they bounce and the right side shows the cars after they bounce. The vector beside each car represents the velocity of the car at that instant.
Figure 2.12.1. Two bumper cars before and after a collision.
Is the magnitude of the average acceleration of the top bumper car greater than, less than, or equal to the magnitude of the average acceleration of the bottom bumper car?
Tip: Sketch vectors to represent the change in velocity for each bumper car to support your reasoning.

Subsubsection Calculation Activities

A*R*C*S 2.12.3. The 100-meter Dash.

In a race with a total distance of \(d = 100 \mathrm{~m}\text{,}\) the winner is timed at \(t_1 = 11.2 \mathrm{~s}\text{.}\) The second-place finisher’s time is \(t_2 = 11.6 \mathrm{~s}\text{.}\) How far is the second-place finisher behind when the winner crosses the finish line? Assume the velocity of each runner is constant throughout the race.
(a) Analyze and Represent.
  1. Identify known and unknown quantities with both a symbol and a number. In general, when a quantity is stated with a number or symbol, that is a known quantity.
  2. Identify and justify any assumptions.
  3. Sketch and label a diagram showing the runners and the course of the race.
(b) Calculate.
  1. Represent physics principles that will help you solve for the unknown quantities.
  2. Determine a symbolic expression in terms of the given variables.
  3. Plug numbers into your symbolic answer.
(c) Sensemake.
  1. Check the units of your symbolic answer.
  2. Compare your numerical answers to other numbers in the situation. Find at least one other distance to compare it to: should it be bigger or smaller than that other distance? Explain your reasoning.
  3. Use covariational reasoning and the Sensemaking Steps for each of the three given quantities: \(d\text{,}\) \(t_1\text{,}\) and \(t_2\text{.}\)

Subsubsection Metacognitive Reflection

Activity 2.12.4. Building a Memory Aid.

In physics, you are building models that help describe the real world. As you learn more, these models will become more and more detailed and complicated, with many different parts, including a variety of quantities, assumptions, representations, definitions, principles, key skills, and sensemaking strategies.
Create a memory aid that summarizes what you have learned so far in one page or less. Your goal is to create a reference you can use to quickly and easily find the information (say, during a quiz or exam) to answer the types of activities you have complete so far. How you structure your model is up to you, but organization is important for quickly retrieving information.

References References

[1]
The 100-meter Dash activity adapted from Openstax: https://openstax.org/books/university-physics-volume-1/pages/3-challenge-problems.