Module 9  Velocity  
Introduction  Lesson 1  Lesson 2  Lesson 3  Self Test  
Lesson 9.1: Average Velocity  
In this lesson you will calculate and compare average velocities of a falling object over several different time intervals and then graphically illustrate these velocities. The following experiment was conducted to illustrate the concept of average velocity. The data from the experiment will be used to create a scatter plot and to find average velocities. An Experiment: Dropping a Book A book was dropped from a height of 0.865 meters and its height above ground was monitored with a Texas Instruments CalculatorBased Laboratory™ (CBL™). The following table contains data of the book's height in meters versus time in seconds.
Entering the Data To create a scatter plot of the data and explore average velocities, the data must be entered into the Stat List editor.
Making a Scatter Plot of Height (y) versus Time (x)
Average Velocity Average velocity is defined to be the change in position divided by elapsed time. If h_{1} is the height at time t_{1} and h_{2} is the height at time t_{2} : h_{2}  h_{1} represents change in position, t_{2}  t_{1} represents elapsed time, and represents average velocity. Finding the Average Velocity Find the average velocity of the book from t = 0 to t = 0.28 by using the points (0, 0.865) and (0.28, 0.454).
The average velocity over the interval from t = 0 to t = 0.28 was approximately 1.468 m/s. The negative sign means that the object is moving downward. Finding the Average Velocity over Subintervals 9.1.1 Approximate the average velocity
Click here for the answer. 9.1.2 The second average velocity has a larger magnitude than the first. Describe what this tells you about the falling object. Click here for the answer. Slope as Average Velocity Compare the following two expressions.
Because slope and average velocity are computed the same way, the average velocity from t = 0 to t = 0.28 can be represented as the slope of the line through the corresponding points on the scatter plot. Drawing Line Segments To illustrate the average velocity between two points, you can graph a line segment through the points with the Line command, which is found in the Draw menu. Draw the line segment through the points that represent t = 0 and t = 0.28.
The syntax for the Line command is Line(x1,y1,x2,y2) and the two points are (0, 0.865) and (0.28, 0.454).
The slope of this line segment is the average velocity for the entire time interval given in the table.
Illustrating Average Velocities on Subintervals The average velocity of the book during the subinterval from t = 0 to t = 0.16 can be illustrated by drawing the line segment that contains the points (0, 0.865) and (0.16, 0.716).
Illustrate the average velocity between t = 0.16 and t = 0.28 by drawing the line segment between the points (0.16, 0.716) and (0.28, 0.454).
The slope of each line segment is the average velocity over the corresponding time interval. Clearing the Line Segments


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