Unit 2: Graphical Relationships Sprayberry Physics

Physics Comp Book UNIT 2: Graphical Relationships Copy GPS listed on the LTA. Circle the verbs; underline the nouns. Page Contents 10 Concept Map: Graphical Relationships 11 independent variable / dependent variable 12 x-axis, y-axis 13 slope / 14 Example: Translating Graphs 15 Lab SUMUPS: * Moving Man Internet Lab * Running Man

Concept Map: Graphical Relationships Rise Run Graphing Basics Slope X-axis Y-axis independent & dependent variables Reading graphs = velocity! on position vs. time on velocity vs. time = acceleration! on acceleration vs. time = zero (in our class)

Graphing Basics: Labeling the axes Scientists have rules for choosing which variable is graphed on which axis. On the X-axis (horizontal) is the independent variable On the Y-axis (vertical) is the dependent variable Which is the x-axis and which is y-axis?

Graphing Basics: indep vs. dep variables So what are the independent variable and dependent variables? The independent variable is not affected by the changing dependent variable. The dependent variable changes as the independent variable. In other words, the dependent variable DEPENDS on the independent variable. Independent or dependent? Time vs. position Time vs. velocity Time vs. acceleration Where would these go on the graph?

Graphing Basics: more on variables… Time (as in a particular moment in time) is TYPICALLY the INDEPENDENT variable. In this class, if time is graphed, it is on the x-axis. Think about it: nothing stops time. Time doesn’t change with speed; speed changes with time. Independent or dependent? Time vs. position Time vs. velocity Time vs. acceleration Where would these go on the graph?

Frayer Models for: x, y axis & independent and dependent variables Picture: Definition: How to remember: Examples:

Graphing Basics: Slope The slope of a line describes its steepness. It is the ratio of the vertical change (called the rise) to the horizontal change (called the run). slope = rise vertical change run horizontal change Let’s look at the slope of this line: We can use any two points on the line (the slope of a line is constant). What is the rise? What is the run?

Finding slope --practice Another example: Find the slope— slope = rise vertical change run horizontal change

Use a DISTANCE/TIME GRAPH Steeper the slope = faster the speed GRAPHING MOTION Use a DISTANCE/TIME GRAPH -Time = X axis -Distance = Y axis A graph of constant speed will represent the motion with a straight line To show two constant speeds which are different, you use SLOPE = steepness of the line = speed Steeper the slope = faster the speed

Constant Versus Changing Speed time time CONSTANT SPEED CHANGING SPEED

A graph of changing speed will have a zig-zag or curved line GRAPHING MOTION A graph of changing speed will have a zig-zag or curved line

Putting it all together FASTEST CONSTANT SPEED DISTANCE SLOWER CONSTANT SPEED What is the slope of this part of the line? CHANGING SPEED TIME

Putting it all together What is the average speed (slope) during the 10 min to 20 min period? 1000 600 Change in distance = 1200-600 = 600m Amount of time = 20-10 = 10 min 200 Avg. Speed = change in distance (600 m) Amount of time (10 min) 10 20 30 = 60 m/min

Frayer for Slope Picture: Definition: How to calculate: What to remember:

What does slope mean?