Foundations of Physics CPO Science Foundations of Physics Chapter 9 Unit 1, Chapter 3

Unit 1: Measurement and Motion Chapter 3: Models of Motion 3.1 Speed 3.2 Observations of Motion 3.3 Analyzing Motion with Graphs

Chapter 3 Objectives Calculate time, distance or speed when given two of three values. Identify the variables in an experiment. Design an experiment where all the variables but one are controlled. Draw and interpret graphs of experimental data including speed versus position, speed vs. time, and position vs. time. Use a graphical model to make predictions that can be tested by experimenting. Determine speed from the slope of a position versus time graph. Determine distance from the area under a speed versus time graph.

Chapter 3 Vocabulary Terms speed distance time variables model initial speed angle friction experimental variable control variables trial experimental technique procedure dependent variable y-axis x-axis independent variable graphical model graph position origin rate slope average speed instantaneous speed

3.1 Speed Key Question: What is speed and how is it measured? *Students read Section 3.1 AFTER Investigation 3.1

3.1 Speed Distance traveled (m) Speed (m/sec) v = d t Time taken (sec)

3.1 Calculate speed A bird is observed to fly 50 meters in 7.5 seconds. Calculate the speed of the bird in m/sec. 1) You are asked to find speed in m/sec. 2) You are given the distance in m and time in sec. 3) v = d÷t 4) v = 50 m ÷ 7.5 sec = 6.67 m/sec

3.1 Calculate distance How far do you go if you drive for 2 hours at a speed of 100 kilometers per hour? 1) You are asked for distance. 2) You are given time in hours and speed in km/h. 3) d = vt 4) d = 2 hrs × 100 km/h = 200 kilometers

3.1 Calculate time and distance A space shuttle is traveling at a speed of 7,700 m/sec. How far does the shuttle travel in kilometers in one hour? At an altitude of 300 kilometers, the circumference of the shuttle’s orbit is 42 million meters. How long does it take the shuttle to go around the Earth one time? 1) This is a two-part problem asking for distance in kilometers and time in hours 2) You are given a speed and time for the first part, and a speed and distance for the second. 3) d = vt, and t = d ÷ v 1 hour = 3,600 seconds 1 km = 1,000 m 4) Part 1: d = (7,700 m/sec)(3,600 sec) = 27,720,000 m Convert to kilometers: = 27,720,000 ÷ 1,000 = 27,720 km Part 2: t = 42 × 106 m ÷ 7,700 m/sec = 5,455 seconds Convert to minutes: 5,455 ÷ 60 = 90.9 minutes

3.1 Units for Speed

3.1 Calculating Speed Why the letter v is used for speed... We use the letter v to represent speed in a formula. If this seems confusing, remember that v stands for velocity. Speed is a single measurement that tells how fast you are going, like 100 km/h. Velocity means you know both your speed and your direction.

3.2 Observations of Motion Key Question: Can you predict the speed of a ball rolling down a ramp? *Students read Section 3.2 AFTER Investigation 3.2

3.2 Observations of Motion Variables that can affect the speed of a marble.

3.2 Observations of Motion Experimental Techniques Control and experimental variables are important in controlled experiments.

3.2 Observations of Motion Experimental Techniques Experimental technique is how you actually do the experiment. Each time you run the experiment is called a trial. Data for three trials

3.2 Observations of Motion Scientific results must always be repeatable. A procedure is a collection of all the techniques used to do an experiment. Writing good procedures is the best way to ensure that others can repeat and verify your experiments. A sample procedure

3.2 Graphical Data To a scientist, a graph is a language that shows the relationship between two variables. By convention, graphs are drawn a certain way just like words are spelled certain ways. This graph shows the relationship between speed and distance.

3.2 Graphical Data Speed, the dependent variable goes on the y-axis. Distance is the independent variable and goes on the horizontal or x-axis. This graph shows the relationship between speed and distance.

3.2 Using graphical models If the graph is created from accurate data, the prediction will also be accurate.

3.2 Recognizing relationships in data Cause and effect Patterns indicate relationships Strong relationship between variables NO relationship between variables

3.2 Recognizing Relationships in Data

3.3 Analyzing Motion with Graphs Key Question: How do you model motion? *Students read Section 3.3 AFTER Investigation 3.3

How to make a graph Decide what to put on the x and y axes. Make a scale by counting boxes to fit your largest value (multiples of 1, 2, 5 or 10 are best). Plot your points. Draw a best fit curve. Create a title and label each axis. Speed vs. Distance

3.3 Position time graph A position versus time graph shows a more detailed history of the drive, including when the car was moving, and when it was stopped. The graph shows that during the first hour, your position gradually increased from your initial position (0 miles) to a point 60 miles away. It then shows that you were stopped between 1 hour and 1.5 hours because your position didn’t change. Finally, the graph shows that you started driving again at 1.5 hours and changed your position until you reached a point 90 miles away from your starting point. The graph contains much more information because it shows the instantaneous speed all through the trip.

3.3 Interpret a position time graph The position versus time graph shows a boat traveling through a long canal. The boat has to stop at locks for changes in water level. a) How many stops does the boat make? b) What is the boat’s average speed for the whole trip? c) What is the highest speed the boat reaches? A position versus time graph shows a more detailed history of the drive, including when the car was moving, and when it was stopped. The graph shows that during the first hour, your position gradually increased from your initial position (0 miles) to a point 60 miles away. It then shows that you were stopped between 1 hour and 1.5 hours because your position didn’t change. Finally, the graph shows that you started driving again at 1.5 hours and changed your position until you reached a point 90 miles away from your starting point. The graph contains much more information because it shows the instantaneous speed all through the trip.

3.3 Slope The slope of a line is the ratio of the “rise” (vertical change) to the “run”(horizontal change) of the line.

3.3 Constant Speed On this graph, a constant speed is a straight horizontal line.

Application: Slow-motion Photography