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Foundations of Physical Science
Unit 1: Forces and Motion
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Chapter 2: Mathematical Models
2.1 Using a Scientific Model to Predict Speed 2.2 Position and Time 2.3 Acceleration
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Learning Goals Construct a speed vs. distance graph.
Use a graph to make a prediction that can be quantitatively tested. Calculate the percent error between a measurement and a prediction. Create and analyze a distance vs. time graph.
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Learning Goals (continued)
Determine the slope of a line. Distinguish between linear and nonlinear graphs. Distinguish between speed and acceleration. Calculate acceleration from a formula. Calculate acceleration from the slope of a speed vs. time graph.
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Vocabulary accelerate acceleration average speed conceptual model
deceleration dependent variable free fall graphical model gravity independent variable physical model scientific model
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2.1 Using a Scientific Model to Predict Speed
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Can you predict the speed of the car at any point on the ramp?
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Scientific Models A model that shows how each variable from an experiment relates to another Mental models Physical models Conceptual models Graphical models
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Making a Graphical Model
A graph shows a relationship between the variable on the x-axis and on the y-axis Graphs use numbers and are considered “mathematical models” Dependent variable (y-axis) Independent variable (x-axis)
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Making a Graphical Model
Decide what to put on the x and y axis. Make a scale for each axis by counting boxes to fit your largest value. Plot your points by finding the x value, and drawing a line up until you get to the right y value. Put a dot for each point.
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Making a Graphical Model
Draw a smooth curve that shows the pattern of the points. Don’t simply connect the dots. Make a title for your graph.
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Reading a Graph Graphs organize your data into a model you can use to make predictions
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Cause and Effect Relationships
How does one variable effect another? Graphs are a good way to see whether there is a connection or not
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Cause and Effect Relationships
Strong Weak Inverse
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2.2 Position and Time
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Position Position (Displacement)- comparison from starting point, includes direction Distance- interval of length without regard to direction Position and Distance-not the same thing!
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Determining Speed from the Slope of a Graph
Slope is the ratio of “rise” (vertical change) to the “run” (horizontal change) of a line. The rise is determined by finding the height of the triangle shown. The run is determined by finding the length along the base of the triangle
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Speed The slope of the position vs. time graph
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Instantaneous and Average Speed
Does your speed stay exactly the same during a real trip? Average Speed: total distance divided by the total time taken (Initial velocity + Final velocity) 2 Instantaneous Speed: the speed you have at a specific point in your journey; use a position vs. time graph
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2.3 Acceleration
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Acceleration The rate at which velocity/speed changes with time
Change: magnitude, direction or both a = change of velocity/time interval
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Force Causes Acceleration
To accelerate an object, it has to be pushed or pulled…a force is applied Force can be: Sudden Steady (i.e. gravity)
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Acceleration a = (Vf - Vi)/t Vf = Final Velocity Vi = Initial Velocity
t = time
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Acceleration Slope of the speed-time graph = acceleration
> slope = > acceleration
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Deceleration (Negative Acceleration)
< slope = < acceleration
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No Acceleration (Constant Velocity)
Zero acceleration = straight line on the speed-time graph constant speed = no acceleration
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Acceleration
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The Units of Acceleration
Usually done in metric units Change in speed divided by change in time 5 Meters per second per second (m/s/s) 5 Meters per second squared (m/s2) The speed is increasing by 5 m/s every second
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Free Fall A state of fall under the influence of only gravity
Free from air resistance
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Free Fall The amount of acceleration is the same for all freely falling objects in the same vicinity Freely falling objects gain speed at the rate of 9.8 m/s each second (9.8 m/s2)
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