This page offers a clear explanation of the equations that can be used to describe the one-dimensional, constant acceleration motion of an object in terms of its three kinematic variables: velocity, displacement, and time. A set of problems accompanies the text, giving students practice in conceptual, algebraic, calculus-based, and statistical questions. This is part of an online textbook in introductory physics.
9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments.
9. The Mathematical World
9B. Symbolic Relationships
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/H3. Make up and write out simple algorithms for solving real-world problems that take several steps.
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)
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 or computational representations of phenomena to describe explanations. (9-12)
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)
Seeing Structure in Expressions (9-12)
A-SSE.2 Use the structure of an expression to identify ways to rewrite it.
A-SSE.3.c Use the properties of exponents to transform expressions for exponential functions.
Creating Equations? (9-12)
A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Reasoning with Equations and Inequalities (9-12)
A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
High School — Functions (9-12)
Linear, Quadratic, and Exponential Models? (9-12)
F-LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12
Range of Reading and Level of Text Complexity (6-12)
RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9—10 text complexity band independently and proficiently.
%0 Electronic Source %A Elert, Glenn %D July 18, 2006 %T The Physics Hypertextbook: Equations of Motion %V 2017 %N 28 June 2017 %8 July 18, 2006 %9 text/html %U http://physics.info/motion-equations/
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