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Motivating Calculus-Based Kinematics Instruction with Super Mario Bros
Here are the resources you will need for the AP Calculus AB free response questions. Be sure to try out the prior year questions and check out the video solutions. Working through these problems is an important part of your FRQ test prep. In this article, I describe a problem-based approach to calculus-based kinematics instruction that contextualizes students' learning within the Super Mario Bros. Video game—a game that is more than 20 years old, but still remarkably popular with today's high school and college students.
Abstract
High-quality physics instruction is contextualized, motivates students to learn, and represents the discipline as a way of investigating the world rather than as a collection of facts and equations. Inquiry-oriented pedagogy, such as problem-based instruction, holds great promise for both teaching physics content and representing the process of doing real science.2 A challenge for physics teachers is to find instructional contexts that are meaningful, accessible, and motivating for students. Today's students are spending a growing fraction of their lives interacting with virtual environments, and these environments—physically realistic or not—can provide valuable contexts for physics explorations3-5 and lead to thoughtful discussions about decisions that programmers make when designing virtual environments. In this article, I describe a problem-based approach to calculus-based kinematics instruction that contextualizes students' learning within the Super Mario Bros. video game—a game that is more than 20 years old, but still remarkably popular with today's high school and college students.
- computer games;
- kinematics;
- physics education;
- 01.50.ht;
- 01.50.ff;
- 45.40.-f;
- 45.50.-j;
- Instructional computer use;
- Films;
- electronic video devices;
- Dynamics and kinematics of rigid bodies;
- Dynamics and kinematics of a particle and a system of particles
Have you ever wondered what the difference is between distance and displacement?
Mario Particle Motion Ap Calculus 2018 Problems
Look no further!
Distance is the amount traveled, regardless of any change in direction along the way, while displacement is just the amount span or interval between the starting point and ending point.
The Physics Classroom rightly compares these two ideas by stating that distance is a scalar or length, that refers to how much ground an object has covered during its motion, while displacement is a vector with length and direction, and refers to an object's overall change in position.
Simple enough, right?
But you know what is so confusing for students? Sometimes textbooks and professors use different terminology in expressing length and motion!
In some instances, the word distance will be used to describe displacement, and the phrase total distance will be used in place of the word distance.
So how will we know the difference?
There are some easy tricks for figuring out what a question is talking about, and this video will clear up any confusion.
In physics and calculus courses alike, the concept of distance and displacement, and how it relates to acceleration, velocity, and position is called the study of particle motion, and utilizes the definite integral.
We will draw upon our previous knowledge of how to find critical numbers to determine when a particle is at rest and if/when it changes direction.
Then we will learn how to write definite integrals given an initial condition and a derivative expression, and use the integral expression to find both distance and displacement.
Finally, we will look at a Free Response Question where we will use most of our derivative and integral techniques, as this question will ask us to find the:
- instantaneous rate of change
- average rate of change
- increasing and decreasing intervals
- definite integral expression for displacement
- average value function
- total distance
Particle Motion Video
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