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Name: _____________________________________________ Period: _____ Physics Unit I: Motion Subunit A: Constant Velocity Motion Maps, graphs and equations can describe and predict motion. Equations Variables, Units NOTES: Unit I-A Objectives What you should know when all is said and done 1. You should distinguish between a scalar and a vector: a. know the difference between distance and displacement. b. know the difference between speed and velocity. c. know the difference between average and instantaneous speed and velocity. 2. You should be able to determine the average velocity of an object in two ways: a. determining the slope of an x vs t graph. b. using the equation v = Δx/Δt 3. You should be able to determine the displacement of an object in two ways: a. finding the area under a v vs t graph. b. using the equation Δx = vt 4. Given a motion map, you should be able to: a. describe the motion of the object (starting position, direction of motion, velocity) b. draw the corresponding x vs t graph 5. Given an x vs t graph, you should be able to: a. describe the motion of the object (starting position, direction of motion, velocity) b. draw the corresponding v vs t graph c. draw a motion map for the object. d. determine the average velocity of the object (slope). e. write the mathematical model which describes the motion. 6. Given a v vs t graph, you should be able to: a. describe the motion of the object (direction of motion, how fast) b. draw the corresponding x vs t graph c. determine the displacement of the object (area under curve). d. draw a motion map for the object. e. write a mathematical model to describe the motion. Unit I-A: Constant Velocity Worksheet 1 1. When choosing a 1-dimensional horizontal reference frame, or coordinate system, we usually choose the positive direction to be toward the (right / left) and the negative direction to be toward the (right / left). 2. ______ A quantity that only describes how much (magnitude) is referred to as a A) scalar quantity B) vector quantity 3. ______ A quantity that describes how much (magnitude) and which way (direction) is referred to as a A) scalar quantity B) vector quantity 3. Some examples of scalars are: 4. Some examples of vectors are: 5. To measure displacement, or change in position Δx, A) measure every meter moved B) take the final position minus the initial position only 6. True or False: An object can be moving for 10 seconds and still have zero displacement. 7. True or False: It is possible for an object to move for 10 seconds at a high speed and end up with negative displacement. 8. Johnny drives to 1920 miles in 32 hours and returns home by the same route in the same amount of time. A) Determine his average speed. B) Determine his average velocity. C) Compare these two values and explain any differences. 9. This person has a displacement of ________ km. a. 0 km b. 3 km c. 3 km, E d. 3 km, W e. 5 km f. 5 km, N g. 5 km, S h. 6 km i. 6 km, E j. 6 km, W k. 31 km l. 31 km, E m. 31 km, W n. None of these. 9. AAcross-country skiermoves movesfrom from location A location to location to location C to location D. leg Each leg 10. cross-country skier location A to B toBlocation C to location D. Each of the of the back-and-forth motion takes 1 minute to complete; the total time is 3 minutes. back-and-forth motion takes 1 minute to complete; the total time is 3 minutes. A) What is the distance skierduring duringthe thethree three minutes of recreation? a. What is the distancetraveled traveled by by the the skier minutes of recreation? b. What is the net displacement of the skier during the three minutes of recreation? B) What is the net displacement of the skier during the three minutes of recreation? c. What is the displacement during the second minute (from 1 min. to 2 min.)? C) What is the displacement during the second minute (from 1 min. to 2 min.)? d. What is the displacement during the third minute (from 2 min. to 3 min.)? D) What is the displacement during the third minute (from 2 min. to 3 min.)? E) Calculate the average speed (in m/min) and the average velocity (in m/min) of the skier during the three minutes of recreation. © The Physics Classroom, 2009 10. Page 2 Position (m) 10 A) Equation: _______________________ B) This object starts ______ meters to the (right / left) of the origin and travels with ______________ ______________ in a straight line in the (+ / - ) direction for 10 seconds at a speed of ____________. Time (s) 0 0 10 11. Position (m) A) Equation: 10 B) This object starts ______ meters to the (right / left) of the origin and travels with ______________ ______________ in a straight line in the (+ / - ) direction for 10 seconds at a speed of ____________. Time (s) 0 0 10 12. Position (m) 0 Time (s) A) Equation: B) Describe the motion of this object as above. -10 0 10 UNIT II READING: MOTION MAPS A motion map represents the position, velocity, and acceleration of an object at various clock readings. (At this stage of the class, you will be representing position and velocity only.) Unit I-A Reading: Motion Maps & Graphs Suppose that you took a stroboscopic picture of a car moving to the right at constant velocity A motion mapimage represents thethe position, acceleration of an object at various clock where each revealed positionvelocity, of the carand at one-second intervals. readings. (At this stage of the class, you will be representing position and velocity only.) Suppose that you took a stroboscopic picture of a car moving to the right at constant velocity where each image revealed the position of the car at one-second intervals. This is the motion map that represents the car. We model the position of the object with a small point. At each position, the object’s velocity is represented by a vector. This is the motion map that represents the car. We model the position of the object with a small point. At each position, the object’s velocity is represented by a vector. If the car were traveling at greater velocity, the strobe photo might look like this: If the car were traveling at greater velocity, the strobe photo might look like this: The corresponding motion map has the points spaced farther apart, and the velocity vectors are longer, implying that the car is moving faster. The corresponding motion map has the points spaced farther apart, and the velocity vectors are longer, implying that the car is moving faster. If the car were moving to the left at constant velocity, the photo and motion map might look like If the this:car were moving to the left at constant velocity, the photo and motion map might look like this: More complicated motion can be represented as well. More complicated motion can be represented as well. Here, an object moves to the right at constant velocity, stops and remains in place for two seconds, then moves to the left at a slower constant velocity. Here, an object moves to the right at constant velocity, stops and remains in place for two seconds, then moves to the left at a slower constant velocity. 'Modeling Workshop Project 2002 1 Unit II Reading-Motion Maps v2.0 Consider the interpretation of the motion map below. At time t = 0, cyclist A starts moving to Consider interpretation motion maptobelow. Atoftime = 0, cyclist A starts moving to the right atthe constant velocity,of atthe some position the right the torigin. the rightthe at constant velocity, at some position to the At right of the origin. Consider interpretation of the motion map below. time t = 0, cyclist A starts moving to the right at constant velocity, at some position to the right of the origin. Cyclist B starts at the origin and travels to the right at a constant, though greater velocity. Cyclist B starts the origin andboth travels the same right at constant, greater velocity. At t =B 3 starts s, B overtakes A (i.e., have the but though Bthough is moving faster). Cyclist atatthe origin and travels totothe right atposition, aaconstant, greater velocity. At t = 3 s, B overtakes A (i.e., both have the same position, but B is moving faster). At t = 3 s, B overtakes A (i.e., both have the same position, but B is moving faster). graphicalrepresentation representationof ofthe thebehavior behavior of ofcyclists cyclistsAAand andBBwould wouldlike likethis: this: AAgraphical A graphical representation of the behavior of cyclists A and B would like this: You could also represent the behavior algebraically as follows: You could could also alsorepresent representthe thebehavior behavior algebraically follows: You algebraically asas follows: x = v At + x0 , for A = vvAtt + xx = + xx0,, forfor A A where vB > vA x x= =vBAvt,Bt, 0 for forBBwhere v B > vA x = vBt, for B Throughout semester, you will be representing the behavior of objects in motion in multiple where vB > vthis A Throughout this semester, you will be representing the behavior of objects in motion in multiple ways: diagramatically (motion maps), graphically and algebraically. ways: diagramatically (motion andthe algebraically. Throughout this semester, youmaps), will begraphically representing behavior of objects in motion in multiple ways: diagramatically (motion maps), graphically, and algebraically. Hints on drawing your own motion maps: 1. Draw dots indicating the position of the object at equal time intervals, i.e. each second. 2. Attach arrows to the dots indicating the direction of motion. Make the arrow length half of the space between the dots to make your motion map easy to read. 3. When an object is stopped for several time intervals, draw multiple dots at the same position. 4. Make sure your sequence of arrows has a logical flow so that the motion is clearly communicated. Unit I-A: Constant Velocity Worksheet 2 1. Consider the position vs. time graph below for cyclists A and B. A) Do the cyclists start at the same point? How do you know? If not, which is ahead? x (m) A B B) At t = 7 s, which cyclist is ahead? How do you know? C) Which cyclist is traveling faster at t = 3 s? How do you know? 5 t (s) D) Are their velocities equal at any time? How do you know? E) What is happening at the intersection of line A and B? F) Draw a motion map for cyclists A and B. 2. Consider the position vs. time graph below for cyclists A and B. A) How does the motion of the two cyclists in this graph compare to the previous question? B) Which cyclist has the greater speed? How do you know? D) Which cyclist has traveled further during the first 5 seconds? How do you know? F) Draw a motion map for cyclists A and B. 3. A) Using the Data Table below, create a graph and write the corresponding equation Time (s) 0 1 2 3 4 5 Position (m) 15 12 9 6 3 0 B) Find the equation of the line. C) Describe the motion of the object. D) Draw a motion map for the object. 4. The graph at below shows the motion of a girl on a jet ski moving in a straight line. A) What is the total distance she travels? B) What is her total displacement? C) What is her average speed? D) What is her average velocity? Unit I-A: Constant Velocity Worksheet 3 1. A motorized scooter was observed to be at the following positions at the times listed below: t (s) x (m) 0 11 1 9 2 7 A) Draw a motion map for 3 5 the scooter. 4 3 5 1 B) Plot the position vs. time graph for the scooter. C) Was the scooter’s velocity constant throughout the whole interval? How do you know? D) What is the velocity of the scooter? How do you know? E) What would his position be at t = 7 s if his velocity remains constant? Use your equation to find out. 2. Robin, roller-skating down a sidewalk, was observed to be at the following positions at the times listed below: t (s) x (m) 0 2 A) Plot a position vs. time graph for the 1 5 skater. 2 8 5 14 8 20 10 26 B) Find the velocity of the skater. C) What is the equation that models her motion? D) How far from the origin was she at t = 6 s? How do you know? E) What would be her position at t = 12 seconds if her velocity remains constant? 3. The following data were obtained for the skater’s second trial: t (s) 0 2 4 6 8 10 x (m) 4 10 16 22 28 34 A) Plot the position vs. time graph for the skater. B) Find the velocity of the skater. C) What is the equation that models her motion? D) How far from the origin was she at t = 5 s? How do you know? E) What would be her position at t = 12 seconds if her velocity remains constant? 4. A spider runs back and forth in a straight line with the following data obtained: t (s) x (m) 0 4 2 4 6 8 10 12 6 12 12 8 4 0 A) Plot the position vs. graph for the spider. time B) What do you think is happening during the interval: t = 4s to t = 6 s? How do you know? time C) What do you think is happening during time interval t = 6s to t = 12s? How do you the know? D) Determine the spider’s average speed from t = 0s to t = 12s. E) Determine the spider’s average velocity from t = 0s to t = 12s. 5. The spider is now seen to move in the following manner: t (s) x (m) 0 8 A) Plot the position vs. time graph for the 2 7 spider. 4 6 6 6 8 8 10 10 12 12 B) During what time interval is the spider traveling the fastest? How do you know? C) What do you think is happening during the time interval t = 4s to t = 6 s? How do you know? D) Determine the spider’s average speed from t = 0s to t = 12s. E) Determine the spider’s average velocity from t = 0s to t = 12s. 6. This data table shows information about two toy cars that were raced side-by-side. t (s) 0 1 2 3 4 5 6 7 8 9 10 x1 (m) 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 x2 (m) 0 1 2 3 4 5 6 7 8 9 10 A) Draw a motion map of each one, one above the number line and the other below the number line showing which car is which. B) Draw a graph of both cars on C) Find the velocity of each toy car. Show your work. the same graph. Constant VelocityVelocity Model Worksheet 3: Unit I-A: Constant Velocity vs. Time Graphs and Displacement Worksheet 4 1. This motion map shows the position of an object once every second. From the motion map, 1. Use the motion to answer the following questions. answermap the below following: a. Describe the motion of the object. A) What can you conclude about the motion of the object? B) Draw position-time and velocity-time graphs for the object on the graphs below. Represent Positionb.(m) the motion with a quantitativeVelocity x vs t graph. (m/s) c. Represent the motion with a quantitative v vs t graph. Time (s) Time (s) d. Write a mathematical expression that represents the relationship C) Write mathematical expressions that represent the relationships betweenbetween positionposition and timeand time. and between velocity and time for the object. e. Write a mathematical expression that represents the relationship between velocity and time. D) Describe what the area under the line in velocity-time graph represents. Crosshatch this area. f. Cross hatch the area under the velocity-time graph. What are the units of this area? Describe what the area under the v-t graph represents and find its value. 2. Use the position-time data below to answer the following questions. t (s) x (m) 0 0 1 2 2 4 Velocity 3 4(m/s) 4 7 5 10 6 10 7 10 8 5 9 0 A) Construct a position vs. time graph and a velocity vs. time graph for this data. Position (m) Time (s) 14(s) Time C) Determine the displacement from t = 3.0 s to 5.0 s using the velocity-time graph. Show on the graph what you did and explain your thinking. D) Determine the displacement from t = 7.0 s to 9.0 s using the velocity-time graph. Show on the graph what you did and explain your thinking. E) Compare your results to the position-time graph. Do the two results match? Unit I-A: Constant Velocity Worksheet 5 1. Sketch the velocity vs. time graph and the motion map corresponding to the following descriptions of the motion of an object. 6. Sketch velocity vs. time graphs and motion maps corresponding to the following descriptions of the motion of an object. Theobject objectisismoving movingaway in thefrom positive direction A)a.The the origin at a at a constant (steady) speed. constant (steady) speed. Motion Map: 0 m 6. Sketch velocity vs. time graphs and motion+ maps corresponding to the following descriptions of t im e the motion of an object. a. The object is moving in the positive direction at a (steady) speed.still. B) constant The object is standing b. The object Motion Map: is standing still. 0 m Motion Map: 0 m + tim edescriptions of 6. Sketch velocity vs. time graphs and motion maps corresponding to the following + the motion of an object. Theobject objectmoves is moving in thethe positive direction at speed, C)a.The towards origin at a steady a constant (steady) speed. then it stands still. t im e b. The object is standing still. Motion Map: 0 m Map: Motion c. The object moves in the negative direction at a 0 m steady speed for 10s, then stands still for 10s. + tim e + Motion Map: 0 m tim edescriptions of 6. Sketch velocity vs. time graphs and motion maps corresponding to the following the motion of an object. + D) The object moves away from the origin at a steady speed, a. objectdirection is moving instill. the positive at origin at b. The standing then reverses and moves back direction towards the a constant (steady) speed. the same speed. c. The object Motion Map: moves in the negative direction at a 0 mspeed Motion Map:for 10s, then stands still for 10s. steady 0 m d. The object moves in the positive direction at a + Motion Map: steady + 0 mspeed for 10s, reverses direction and moves back toward the negative direction at the same speed. + Motion Map: 0 m Theobject objectmoves is standing c.b.The in thestill. negative direction at+ a steady speed for 10s, then stands still for 10s. Motion Map: moves in the positive direction at a d. The object 0 mspeed steady Motion Map:for 10s, reverses direction and moves 0 m back toward the negative direction at the same + speed. + ©Modeling Instruction Program 2009 5 Motion Map: 0 m t im e tim e tim e t im e Constant Velocity ws 1 tim e Draw the velocity vs time graphs for for an an object whose motion produced time graphs 2. Draw the velocity vs. time graph object whose motion producedthe theposition distancevsvs. time shown shown below below at left.at left. graphs 5. 6. 7. 8. For many graphs, both the slope of the line and the area between the line and the horizontal axis have meanings. 3. For physical many graphs, both the slope of the line and the area between the line and the horizontal a. What doesphysical the slope of a position time graph tell you about the motion of an object? axis have meanings. A) What does the slope of a position time graph tell you about the motion of an object? b. Looking at the velocity time graphs, determine the units for a square of area on the graph. B) Looking at the velocity time graphs, determine the units for a square of area on the graph. c. What does the the areaarea under the the velocity-time graph tell C) What does under velocity-time graph tellyou youabout aboutthe themotion motion of of an an object? object? ©Modeling Instruction Program 2009 5 Constant Velocity ws2 x t Unit I-A: Constant Velocity Worksheet 6 v Motion map: Fill in the blank boxes with the correct complete information. Constant Velocity Particle Model Worksheet 4: t Multiple Representations of Motion x - t Graph v - t Graph Motion Map Given one motion representation, supply the missing motion representations. 1. Written description: 2. x Written description: x 3. t Written description: x v t Motion map: t v Motion map: 3 6 8 t (s) t v Motion map: 2. Written description: t x 3. Written description: x 4. Written description: t x v 3 6 8 t (s) Motion map: t v Motion map: t t +2 v (m/s) -1 Motion map: 2 4 4. Written description: x t +2 v Motion map: 8 t (s) Written Description The object starts at 2m and moves with a constant positive velocity for two seconds, then stops for 2s, then returns past the starting point at a faster speed in 2s. x - t Graph v - t Graph Motion Map Written Description The object moves with a constant positive velocity for 4 seconds. Then, it stops for 2 seconds and returns to the initial position in 2 seconds. Object A starts 10m to the right of zero and moves to the left at 2m/s. Object B starts at zero and moves to the right at 3 m/s Unit I-A: Constant Velocity Review Worksheet Constant V Vocabulary Terms Coordinate System Displacement Distance Scalar Quantity Vector Quantity Motion Map Average Velocity Average Speed Instantaneous Velocity Re 1. Consider the following position vs. tim Review Problems a. De 1. Consider the position vs. time graph shown. A) Determine the average velocity of the object. b. Wr ob B) Write the mathematical equation to describe the motion of the object. C) Using the equation for the graph, find the position of the object at t = 10 s. 2. Shown below is a velocity vs. time gra 4. A basketball initially travels at 3 m 2. Consider the following v vs. t graph. A) Describe the behavior of the object. a. De B) Draw a motion map to model the behavior of the object. C) How far did the object travel in the interval t = 1s to t = 2s? b. Draw a corresponding position vs. time from the origin.a quantitative motion map b. Draw 0 m c. D) What is the TOTAL displacement? Explain how you got your answer. c. How far did the ball travel from t d. F 5. A racecar reaches a speed of 95 m 3. Use the following graph that represents the motion of a runner for the next 3 questions. A) Describe the motion of the runner during the 25second time interval. B) What distance does the runner travel from 0 – 25 seconds? C) What is the runner’s displacement from 0 – 25 seconds? D) What is the runner’s average speed from 0 – 25 seconds? E) What is the runner’s average velocity from 0 – 25 seconds? 4. A racecar travels at a speed of 95 m/s. How much time does it take to reach the finish line 500 m away? 5. A hummingbird averages a speed of about 28 miles/hour (Cool facts: They visit up to 1000 flowers per day, and reach maximum speed while diving ... up to 100 miles/hour!). Rubythroated hummingbirds take a 2000-mile journey when they migrate, including a non-stop trip across Gulf of Mexico in which they fly for 18 hours straight! How far is the trip across the Gulf of Mexico? 6. Dr. Foster and Mr. Padilla are out skateboarding. The table shows their motion over time. Use the table to answer the questions. Time (s) Position Dr. Foster (m) Position Mr. Padilla (m) 0 0 45 5 10 40 10 20 35 15 30 30 20 40 Position (m) 25 25 50 20 30 60 15 A) Draw a motion map for each skateboarder (one above, one below the line). B) Draw a position-time graph for each skateboarder. C) Does either one of the move at a constant velocity? How administrators do you know? D) Do Dr. Foster and Mr. Padilla same direction? How do you move in the know? E) What is happening at time = 15s? F) How fast is Dr. Foster going? How fast is Mr. Padilla going? Show your work. G) Do you want to join in the fun and skateboard with your administrators? Time (s)