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written by Aaron Titus
These web pages contain problems to supplement the introductory textbook, Matter and Interactions by Ruth Chabay and Bruce Sherwood. These problems are for Volume 1, Chapter 1 on motion and forces. The topics covered include descriptions of motion, vector algebra, and momentum changes. Each problem can be viewed separately, with solutions, or downloaded as a pdf file.

The site includes videos showing solutions to many of the problems. These can be followed with RSS or as podcasts from iTunes. Instructors are encouraged to submit their own problems and solutions to the web site. Problems should be submitted in LaTex.
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Classical Mechanics
- Applications of Newton's Laws
- Linear Momentum
= Collisions in One Dimension
= Conservation of Linear Momentum
- Motion in One Dimension
- Motion in Two Dimensions
- Newton's First Law
General Physics
- Computational Physics
Mathematical Tools
- Vector Algebra
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- High School
- Upper Undergraduate
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- Instructional Material
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This material is released under a GNU General Public License Version 3 license. Materials are submitted by individuals, who retain copyright for their own intellectual property.  Authors must agree to allow free use of their materials for educational purposes, and allow teacher-users to freely redistribute their materials to students and colleagues.
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Aaron Titus
Record Creator:
Metadata instance created December 4, 2009 by Alea Smith
Record Updated:
March 31, 2014 by Caroline Hall
Last Update
when Cataloged:
July 11, 2009
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Next Generation Science Standards

Motion and Stability: Forces and Interactions (HS-PS2)

Students who demonstrate understanding can: (9-12)
  • Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. (HS-PS2-1)
  • Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system. (HS-PS2-2)

Disciplinary Core Ideas (K-12)

Forces and Motion (PS2.A)
  • Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)
  • Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object. (9-12)
  • If a system interacts with objects outside itself, the total momentum of the system can change; however, any such change is balanced by changes in the momentum of objects outside the system. (9-12)

Crosscutting Concepts (K-12)

Scale, Proportion, and Quantity (3-12)
  • Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth). (9-12)
Stability and Change (2-12)
  • Change and rates of change can be quantified and modeled over very short or very long periods of time. Some system changes are irreversible. (9-12)

NGSS Science and Engineering Practices (K-12)

Using Mathematics and Computational Thinking (5-12)
  • Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)
    • Use mathematical representations of phenomena to describe explanations. (9-12)

AAAS Benchmark Alignments (2008 Version)

2. The Nature of Mathematics

2A. Patterns and Relationships
  • 9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

4. The Physical Setting

4F. Motion
  • 9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.
  • 9-12: 4F/H4. Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.
  • 9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.
  • 9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships
  • 9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.
  • 9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.

12. Habits of Mind

12B. Computation and Estimation
  • 9-12: 12B/H2. Find answers to real-world problems by substituting numerical values in simple algebraic formulas and check the answer by reviewing the steps of the calculation and by judging whether the answer is reasonable.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.

High School — Algebra (9-12)

Reasoning with Equations and Inequalities (9-12)
  • A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • A-REI.4.b Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
  • A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

High School — Functions (9-12)

Interpreting Functions (9-12)
  • F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?
  • F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.?
  • F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
  • F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions.
  • F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Linear, Quadratic, and Exponential Models? (9-12)
  • F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
  • F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
  • F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
Trigonometric Functions (9-12)
  • F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.?
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A. Titus, Matter & Interactions Practice Problems: Interactions and Motion, (2009), <>.
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%T Matter & Interactions Practice Problems: Interactions and Motion
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Matter & Interactions Practice Problems: Interactions and Motion:

Is Based On

American Journal of Physics article which discusses the pedagogy behind the Matter and Interactions curriculum, authored by Ruth Chabay and Bruce Sherwood.  May be freely downloaded in pdf format.

relation by Caroline Hall

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