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 \(t_2\text{?}\)
Explanation2.12.2.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.
Figure2.12.1.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?
Sketch vectors to represent the change in velocity for each bumper car.
Explanation2.12.3.Ramp Timing.
You release a ball from rest at the top of a ramp and decide to assume that the ball’s acceleration is constant as it speeds up moving down the ramp. You observe the ball at three times while it is on the ramp: \(t_A = 1.5 \mathrm{~s}\text{,}\)\(t_B = 3.0 \mathrm{~s}\text{,}\) and \(t_C = 4.5 \mathrm{~s}\text{.}\) Using these observations, you determine \(\Delta v_{AB}\) (the change in velocity between \(t_A\) and \(t_B\)) and \(\Delta v_{BC}\) (the change in velocity between \(t_B\) and \(t_C\)).
Is the magnitude of \(\Delta v_{BC}\)greater than, less than, or equal to the magnitude of \(\Delta v_{AB}\text{?}\)
SubsectionCalculation Activities
Activity2.12.4.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)Calculate.
Follow the Calculation Steps: most of the credit will be given for your symbolic calculation.
(b)Sensemake.
Use covariational reasoning and the Sensemaking Steps for each of the three given quantities: \(d\text{,}\)\(t_1\text{,}\) and \(t_2\text{.}\)
SubsectionMetacognitive Reflection
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.
ReferencesReferences
[1]
The 100-meter Dash activity adapted from Openstax: https://openstax.org/books/university-physics-volume-1/pages/3-challenge-problems.
