This applet displays the motion of an object moving with constant acceleration. As a model of a car slowing to a stop, the object initially moves with uniform velocity when brakes are applied. The initial velocity, instant of application of brakes, and braking acceleration can be set by the user. The motion of the object is displayed using a motion diagram and graphs of position and velocity vs. time. This is part of a large collection of physics and math applets by the author.
6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.
9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.
11. Common Themes
6-8: 11B/M4. Simulations are often useful in modeling events and processes.
9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.
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)
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)
NGSS Science and Engineering Practices (K-12)
Developing and Using Models (K-12)
Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)
Use a model to provide mechanistic accounts of phenomena. (9-12)
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
High School — Number and Quantity (9-12)
N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
High School — Algebra (9-12)
Creating Equations? (9-12)
A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
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.
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.5 Interpret the parameters in a linear or exponential function in terms of a context.
%0 Electronic Source %A Reddy, Surendranath %D March 11, 2004 %T Apply the Brakes %V 2014 %N 31 October 2014 %8 March 11, 2004 %9 application/java %U http://surendranath.tripod.com/Applets/Kinematics/Brake/AB.html
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