Use your hypothesis (the mathematical model you created) from activity 4.1 to predict the man s position for the following scenarios:

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1 4.1 Hypothesize Lesson 4: The Moving Man An object is moving in the positive direction at constant velocity v. It starts at clock reading t = 0 sec, at a position x 0. How would you write a function that will allow you to find the position of the object at any time? 4.2 Test Your Idea with Phet Simulations Go to and click on the simulation The Moving Man. (You can get there from Mrs. Kreutter s Physics Links page as well.) You should see a screen like the one shown. There is a man at top of the simulation who can move 10 m in either direction from the origin. The simulation also includes axes of position, velocity and acceleration graphs that will reflect his motion. Since you are not going to use the acceleration or velocity graph right away, you can close them by clicking on the small window in the upper right hand corner of each section. To eliminate the walls, click on special features, then click on free range. Use your hypothesis (the mathematical model you created) from activity 4.1 to predict the man s position for the following scenarios: Scenario 1: The man s initial position is 9 m and he is jogging to the left at 2 m/s. d) Predict the time when he passes through the position at 0m. e) Perform the experiment by entering given quantities in the respective simulation boxes and click Go! Compare your predicted value to the outcome of the testing experiment. Do they agree or disagree? If they disagree, revise your mathematical model of the moving man s motion. Scenario 2: The man is walking at the speed of 0.75 m/s towards his home. When we start observing him, he is at the position of 7 m to the left of the origin.

2 d) Predict the time when he arrives at the house. e) Perform the experiment through the simulation. Compare your predicted value to the outcome of the testing experiment. Do they agree or disagree? If they disagree, revise your mathematical model of the moving man s motion. Scenario 3: When we start observing the man is at the 5 m mark by the house and is running at the speed of 4.5 m/s towards the tree. d) Predict the time when he has traveled 70 m beyond the tree. e) Perform the experiment through the simulation. Compare your predicted value to the outcome of the testing experiment. Do they agree or disagree? If they disagree, revise your mathematical model of the moving man s motion. 4.3 Test Your Idea Use your newly modified hypotheses from the previous activity to predict how you d have to move so that a motion detector creates position versus time graphs that match the graphs in the previous activities. Explain how your prediction compares to the outcome. 4.4 Reason and Represent In this activity you will be acting as the Moving Man or Woman. Below are a number of position vs. time functions and written descriptions. Here you will have to act out how to move so that a motion detector creates position versus time graphs match description provided. Before acting it out, discuss how your motion should match the written and mathematical descriptions. a) A person is 7.0 m away when we start observing and walks towards the origin at 0.4 m/s. b) You are 5.0 m away from the origin at the initial clock reading and walk at 1m/s for 4 seconds towards the origin stop for 3 seconds then walk 0.5 m/s for 6 seconds away from the origin. c) x(t) = 5m +( 0.7m/s)t d) x(t) = 0.8m + (1.2m/s)t

3 Position Kreutter: Kinematics 4 Homework 4.5 Represent and reason m -5.0 m 0.0 m +5.0 m m Examine the dot diagram above. When we start observing the object it is at +7.5 m and moves in the negative direction of the x-axis. a) Describe the motion in words. b) Sketch a position vs. clock reading graph. c) Write a function for the position as a function of time for the object s motion. 4.6 Represent and Reason Thus far, you have represented the motion of a ball with different representations: dot diagrams, words, pictures, tables, and now a graph. Explain how the different representations describe the same motion. a) Use the graph below to describe the motion in words. Pay attention to what happened at zero clock reading! b) Write a function for the position as a function of time for the object s motion. c) You should notice that the two physical quantities on the graph do not have units. Describe a real life situation for this motion if the units were kilometers and seconds. Describe another situation if the units were centimeters and minutes. d) Draw a picture for each of the situations you described in part c Clock Reading 4.7 Equation Jeopardy Three situations involving constant velocity are described mathematically below. 1. ( 86 m) v(1.72 s) ( 100 m) 2. x ( 5.7 m/s)(300 s) (1000 m)

4 3. ( m) ( 5.7 m/s)(6.8 s) x initial a) Write a story or a word problem for which the equation is a solution. There is more than one possible problem for each situation. b) Sketch a situation that the mathematical representation might describe. c) Determine the unknown physical quantity. 4.8 Practice You are learning to drive. To pass the test you need to be able to convert between different speedometer readings. The speedometer says 65 mph. (a) Use as many different units as possible to represent the speed of the car. (b) If the speedometer says 100 km/h, what is the car s speed in mph? 4.9 Practice The speed limit on the roads in Russia is 75 km/h. How does this compare to the speed limit on some US roads of 55 mph? 4.10 Practice Convert the following record speeds so that they are in mph, km/h, and m/s. (a) Australian dragonfly 36 mph; (b) the diving Peregrine falcon 349 km/h; and (c) the Lockheed SR-71 jet aircraft 980 m/s (about three times the speed of sound) Reason You are moving on a bicycle trying to maintain a constant pace. You cover 23 miles in 2 hours. What is your speed in m/s? If you only rode half of the distance maintaining the same pace what would the speed be? If you rode 43 miles, what would the speed be? 4.12 Reason James and Tara argue about speed. James says that the speed is proportional to the distance and inversely proportional to the time during which the distance was covered. Tara says that the speed does not depend on the time or distance. Why would each say what they did? Do you agree with James? Do you agree with Tara? How can you modify their statements so that you could agree with both of them? 4.13 Hair growth speed Physicists often do what is called order of magnitude estimations. Such estimations are approximate calculations of some quantity that they are interested in. For example, how do we estimate the rate that your hair grows in mm/s? Think of the following: How often do you get haircuts? How long does your hair grow during this time? Then convert the time between hair cuts to seconds and the length of your hair growth to millimeters then you are almost done. The question is how will you report your results? What if after dividing length by time you get a number on your calculator that looks like ? How you can report the result so it looks reasonable? A little help Significant digits When we measure a physical quantity, the instrument we use and the circumstances under which we measure it determine how precisely we know the value of that quantity. Imagine that you wear a pedometer and wish to determine the number of steps on average that you make per minute. You walk for 26 min (as indicated by your cell phone) and see that the pedometer shows 2254 steps. You divide

5 2254 by 26 using your calculator and it says If you accept this number, it means that you know the number of steps per minute to within steps/minute. If you accept the number 86.69, it means that you know the number of steps to within 0.01 steps/minute. If you accept the number 90, it means that you know the number of steps within 10 steps/minute. Which answer should you use? The number of the significant digits in the final answer should be the same as the number of significant digits of the quantity used in the calculation that has the smallest number significant digits. Thus, in our example, the average number of steps per minute should be 86, plus or minus 1 steps/minute: 86±1. In summary the precision of the value of a physical quantity is determined by one of two cases. If the quantity is measured by an instrument, then its precision depends on the instrument used to measure it. If the quantity is calculated from other measured quantities, then its precision depends on the least precise instrument out of all instruments used to measure a quantity used in the calculation. Another issue with significant digits arises when a quantity is reported with no decimal points. For example, how many significant digits does 6500 have two or four? This is where the scientific notation helps. Scientific notation means writing numbers in terms of their power of 10. Example: we can write 6500 as 6.5 x This means that the 6500 actually has two significant digits. If we write 6500 as 6.50 x 10 3 it means 6500 had three significant digits. Scientific notation provides a compact way of writing large and small numbers and also allows us to indicate unambiguously the number of significant digits a quantity has Evaluate On the web you might find the following statement: The speed of hair growth is roughly 1.25 centimeters or 0.5 inches per month, being about 15 centimeters or 6 inches per year. With age the speed of hair growth might slow down to as little as 0.25 cm or 0.1 inch a month. Is this result consistent with your estimate? Are the significant figures for different measurements consistent with each other?