scalar: quantity described by magnitude (size) only vector: quantity described by both magnitude AND direction

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1 Unit I: Motion Subunit A: Constant Velocity Chapter 2 Section 1 Texas Physics p Equations Variables, Units NOTES: scalar: quantity described by magnitude (size) only vector: quantity described by both magnitude AND direction

2 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 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. determine the average velocity of the object (slope). d. write the mathematical model which describes the motion. 5. 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. write a mathematical model to describe the motion.

3 Unit I-A: Constant Velocity Worksheet 1 (refer to p.82 Texas Physics for intro to scalar and vector) 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. A cross-country skier moves from location A to location B to location C to location D. Each leg of the back-and-forth motion takes 1 minute to complete; the total time is 3 minutes.

4 9. A cross-country skier moves from location A to location B to location C to location D. Each leg of the back-and-forth motion takes 1 minute to complete; the total time is 3 minutes. A) What is the distance traveled by 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.)? 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 o recreation.

5 10. A) Equation: B) This object starts meters away from the origin and travels with a in the (+ / - ) direction, (away from/towards) the origin, for 10 seconds at a speed of.

6 11. A) Equation: B) This object starts meters away from the origin and travels with a in the (+ / - ) direction, (away from/towards) the origin, for 10 seconds at a speed of.

7 12. A) Equation: B) Describe the motion of this object as above. This object starts -2 meters away from the origin and travels with a constant velocity in the (-) direction, away from the origin, for 8 seconds at a speed of 1 m/s

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?

8 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? 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? D) Are their velocities equal at any time? How do you know? E) What is happening at the intersection of line A and B?

previous question? B) Which cyclist has the greater speed? How do you know?

9 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? C) Which cyclist has traveled further during the first 5 seconds? How do you know?

10 3. A) Using the Data Table below, create a graph and write the corresponding equation Time (s) Position (m) A) Find the equation of the line. B) Describe the motion of the object.

11 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 3 5 4 3 5 1 A) Plot the position vs.

12 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) A) Plot the position vs. time graph for the scooter. B) Was the scooter s velocity constant throughout the whole interval? How do you know? C) What is the velocity of the scooter? Show work. D) 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 1 5 2 8 5 14 8 20 10 26 A) Plot a position vs.

13 2. Robin, roller-skating down a sidewalk, was observed to be at the following positions at the times listed below: t (s) x (m) A) Plot a 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 = 6 s? Show work. E) What would be her position at t = 12 seconds if her velocity remains constant? Show work.

14 3. The following data were obtained for the skater s second trial: t (s) x (m) 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? E) What would be her position at t = 12 seconds if her velocity remains constant?

5. The spider is now seen to move in the following manner: t (s) x (m) 0 8 2 7 4 6 6 6 8 8 10 10 12 12 A) Plot the position vs. time graph for the spider.

16 5. The spider is now seen to move in the following manner: t (s) x (m) A) Plot the position vs. time graph for the spider. 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.

17 6. This data table shows information about two toy cars that were raced side-by-side. t (s) x1 (m) x2 (m) A) Draw a graph of both cars on the same graph B) Find the velocity of each toy car. Show your work.

4. A spider runs back and forth in a straight line with the following data obtained: t (s) x (m) 0 4 2 6 4 12 6 12 8 8 10 4 12 0 A) Plot the position vs. time graph for the spider.

19 4. A spider runs back and forth in a straight line with the following data obtained: t (s) x (m) A) Plot the position vs. time graph for the spider. B) What do you think is happening during the time interval: t = 4s to t = 6 s? How do you know? C) What do you think is happening during the time interval t = 6s to t = 12s? 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.

20 Unit I-A: Constant Velocity Worksheet 4 t (s) x (m) 1. Use the table below to answer the following questions A) Draw position-time and velocity-time graphs for the object on the graphs below Position (m) Velocity (m/s) Time (s) Time (s) B) Write mathematical expressions that represent the relationships between position and time and between velocity and time for the object. C) Describe what the area under the line in velocity-time graph represents. Crosshatch this area.

0 s using the velocity-time graph. Show on the graph what you did and explain your thinking. C) Determine the displacement from t = 7.0 s to 9.

21 2. Use the position-time data below to answer the following questions. A) Construct a position vs. time graph and a velocity vs. time graph for this data. Position (m) t (s) x (m) B) 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. C) 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. D) Compare your results to the position-time graph. Do the two results match? Time (s)

22 Unit I-A: Constant Velocity Worksheet 5 1. Sketch the position vs. time graph and the velocity vs. time graph corresponding to the following descriptions of the motion of an object. A) The object is moving away from the origin at a constant (steady) speed. B) The object is standing still. C) The object moves towards the origin at a steady speed, then it stands still. D) The object moves away from the origin at a steady speed, then reverses direction and moves back towards the origin at the same speed.

23 2. Draw the velocity vs. time graph for an object whose motion produced the distance vs. time graphs shown below at left.

24 3. For many graphs, both the slope of the line and the area between the line and the horizontal axis have physical 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. C) What does the area under the velocity-time graph tell you about the motion of an object?

25 Unit I-A: Constant Velocity Worksheet 6 Fill in the blank boxes with the correct complete information. x - t Graph v - t Graph 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. Object moves with constant negative velocity then turns around and moves with a constrant positive veliocity, then stops. Object moves at constant negative velocity for 3 sec, then stops for 3 sec, then moves at a greater negative velocity towards the origin for 2 seconds. object is still for 2 seconds then moves at 2 m// s for 2 sec in the positive direction. Then slows to 1 m/s in the negative direction.

26 x - t Graph v - t Graph 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. The object starts 5m away from the origin and moves towards the origin with a constant velocity for 2 seconds. Then it stops at 1m from the origin for 2 seconds. Then it turns around and moves away from the origin with half the velocity for 4 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 Object A starts at the origin and moves with a constant positive velocity for 5 seconds. Object B starts 1m away from the origin and moves with the same constant velocity as object A.

27 Unit I-A: Constant Velocity Review Worksheet (Also, practice 1-6 p.42 and 1-6 p.45 Texas Physics) Vocabulary Terms Coordinate System Displacement Distance Scalar Quantity Vector Quantity Frame of reference Average Velocity Average Speed Instantaneous Velocity the velocity of an object at an instant or a specific point in the object's path

28 Review Problems 1. Consider the position vs. time graph shown. A) Determine the average velocity of the object. 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.

29 2. Consider the following v vs. t graph. A) Describe the behavior of the object. B) Draw a position vs. time graph to model the behavior of the object. C) How far did the object travel in the interval t = 1s to t = 2s? D) What is the TOTAL displacement? Explain how you got your answer.

30 A) What distance was traveled between time 2 s and time 6 s? What was the displacement? B) What was the speed between times 2 s and 6 s? What was the velocity? C) What is the distance traveled between time 4 s and time 12 s? What was the displacement? D) What was the average speed between time 4 s and time 12 s? What was the average velocity over this time frame? E) What is the total distance traveled? Total displacement? Average speed? Average velocity?

31 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!). Ruby-throated 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?

32 6. Dr. Foster and Mr. Padilla are out skateboarding. The table shows their motion over time. Use the table to answer the questions. B) Does either one of the administrators move at a constant velocity? How do you know? C) Do Dr. Foster and Mr. Padilla move in the same direction? How do you know? D) What is happening at time = 15s? E) How fast is Dr. Foster going? How fast is Mr. Padilla going? Show your work.

Worksheet 3. Sketch velocity vs time graphs corresponding to the following descriptions of the motion of an object.

Worksheet 3. Sketch velocity vs time graphs corresponding to the following descriptions of the motion of an object. Worksheet 3 Sketch velocity vs time graphs corresponding to the following descriptions of the motion of an object. 1. The object is moving away from the origin at a constant (steady) speed. 2. The object