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Position, Velocity, Acceleration Graphing .
- 1. PR A CTI C E P R O B L E M S Position, Velocity, Acceleration Graphs SPS8. Students will determine relationships among force, mass, and motion. a. Calculate velocity and acceleration.
- 2. Position Graphs 1. Inwhich section(s) was the cart traveling at a constant positive velocity? 2. In which section(s) was the cart traveling at a constant negative velocity? 3. In which section(s) was the cart at rest? 4. In which section did the cart maintain its greatest average speed? How fast was it traveling? 5. How can you tell when the velocity is constant? How can you tell about an objects VELOCITY from a position graph?
- 3. Velocity Graphs 1. Duringwhich time interval(s) did it travel in a positive direction? 2. During which time interval(s) did it travel in a negative direction? 3. Describe the object’s movement between 10 and 15 minutes? 4. What is the car’s acceleration between 10 and 15 minutes? 5. When is the car experiencing an acceleration (+ or -)? How do you know? How can you tell about an object’s ACCELERATION from a velocity graph?
- 4. Position vs. VelocityGraphs Position Graph: (distance) What does a flat, horizontal line mean in terms of: Velocity? Acceleration? What does it mean when the line slopes: Up? Down? What is the difference between the curved and straight sloped lines in terms of velocity and acceleration? Velocity Graph (speed): What does a flat, horizontal line mean in terms of: Position? Acceleration? What does it mean when the line slopes: Up? Down? What is the difference between the curved and straight sloped lines in terms of acceleration?
- 5. Acceleration Graphs 1. Whatdoes a flat, horizontal line mean in terms of: Velocity? Position? 2. What does zero acceleration mean in terms of: Velocity? Position? 3. How would you know from an acceleration graph when velocity is zero? 4. In terms of Newtons’ First Law, what does an acceleration graph tell you about the forces acting on an object?
- 6. Constant Positive Velocity What is happeningwith each graph? •Position? •Velocity? •Acceleration? What is the acceleration when the velocity is constant? Why is the position changing but the velocity remains the same? This object below moves with a constant velocity in the positive direction. •The dot diagram shows that each consecutive dot is the same distance apart (constant velocity). •The position-time graph shows that the slope is both constant (constant velocity) and positive (positive velocity). •The velocity-time graph shows a horizontal line with zero slope (zero acceleration); the line is located in the positive region of the graph (positive velocity). •The acceleration-time graph shows a horizontal line at the zero mark (zero acceleration).
- 7. Constant Negative Velocity What is happeningwith each graph? •Position? •Velocity? •Acceleration? Why does the position graph slope downward? Why is the velocity graph negative? Why is the acceleration graph at zero? This object below moves with a constant velocity in the negative direction. The dot diagram shows that each consecutive dot is the same distance apart (constant velocity). The position-time graph shows that the slope is both constant (constant velocity) and negative (negative velocity). The velocity-time graph shows a horizontal line with zero slope (zero acceleration); the line is located in the negative region of the graph (negative velocity). The acceleration-time graph shows a horizontal line at the zero mark (zero acceleration).
- 8. Positive Velocity with Positive Acceleration Is theobject speeding up or slowing down? Is that positive or negative acceleration? What does the acceleration graph show? What does constant acceleration tell you about the objects velocity? Why is the position line curved upwards? According to Newton’s First Law, what do the graphs tell you about the forces acting on the object? This object below moves in the positive direction with a changing velocity. An object which moves in the positive direction has a positive velocity. If the object is speeding up, then its acceleration vector is directed in the same direction as its motion (in this case, a positive acceleration). The dot diagram shows that each consecutive dot is not the same distance apart (changing velocity). The position-time graph shows that the slope is changing and positive (changing, positive velocity). The velocity-time graph shows a line with a positive (upward) slope (positive acceleration); the line is located in the positive region of the graph (corresponding to a positive velocity). The acceleration-time graph shows a horizontal line in the positive region of the graph (positive acceleration).
- 9. Positive Velocity and Negative Acceleration Is theobject speeding up or slowing down? Is that positive or negative velocity? What does the acceleration graph show? What would happen to the objects movement if the object keeps moving at a constant, negative velocity? According to Newton’s First Law, what do the graphs tell you about the forces acting on the object? This object below moves in the positive direction with a changing velocity. An object which moves in the positive direction has a positive velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a negative acceleration). The dot diagram shows that each consecutive dot is not the same distance apart (changing velocity). The position-time graph shows that the slope is changing positive (changing, positive velocity). The velocity-time graph shows a line with a negative (downward) slope (negative acceleration); the line is located in the positive region of the graph (positive velocity). The acceleration-time graph shows a horizontal line in the negative region of the graph (negative acceleration).
- 10. Graph Practice 1. Whatis on the Y axis? 2. Describe how this object is moving. 3. Does this object ever stop? 4. When is it moving slowest? 5. When is it moving fastest? 6. When does the object have a constant velocity? How do you know? (What does constant velocity look like on a position graph?) 7. What does this tell you about the object’s acceleration?
- 11. Graph Practice 1. Whatis on the Y axis? 2. Between what points is this object at rest? 3. What is happening between points A and B? 4. What is the object doing between points C and D? 5. Between what points is acceleration zero? 6. What happens to the object in terms of Newton’s First Law and forces at each point? 7. What would the position graph look like for this object? Would the line ever go backwards? If so, at what points? 8. What would the acceleration graph look like for this object?
- 12. Graph Practice 1. Betweenwhat points is the velocity constant? 2. At what point is the object at rest? 3. In what direction (positive or negative) is the object moving between points 4 and 5? 4. Between what points does this object move backwards? 5. Is the final position positive or negative? 6. What is the final velocity? How do you know? 7. What would a position graph look like? 8. What would the velocity graph look like?
- 13. 1. CARS INGARAGE – CLASS ACTIVITY 2. SONG: POSITION, VELOCITY, ACCELERATION 3. VELOCITY & ACCELERATION - PRACTICE & PROBLEM SOLVING WORKSHEETS 4. VELOCITY & ACCELERATION GIZMO 5. GRAPHING VELOCITY & ACCELERATION PROBLEMS 6. READ TEXTBOOK – CHAPTER 9 Do problems on page 331 (Relax, there are only 6 of them!) Assignments
- 14. Graphing Activity: Carsin Garage
Editor's Notes
- #2 F-G,G-H B-C, D-E A-B, C-D, E-F D-E – 32 m/s If the line is straight, velocity is constant. If the velocity is increasing or decreasing (acceleration) then the line will be curved.
- #3 0-30 30-55 Moving at a constant velocity of 60 m/min Zero Any time the line is NOT flat and horizontal, there is an acceleration – change in velocity.
- #4 Position: Horizontal, flat line means the object is stopped – zero velocity, zero acceleration Up: moving forward (positive velocity); Down: moving backwards (negative velocity) Straight slope mans the object is moving at a constant velocity – speed is increasing at a steady rate (no acceleration) Curved line means that the object’s velocity is increasing (or decreasing) and there is an acceleration because the velocity is changing Velocity: Any flat, horizontal line means an object is moving at a constant velocity – moving at a steady speed - but no acceleration (Newton’s first law – I keeps doing what it has been doing) Up: increasing speed – positive acceleration; Down: decreasing speed – negative acceleration Straight slope is constant acceleration – speed is changing at a constant rate Curved slope is changing acceleration – speed is changing at an increasing (or decreasing) rate
- #5 Constant positive acceleration means it is moving at an increasing velocity – speeding up – while constant negative velocity means it is moving at a decreasing velocity – slowing down Zero acceleration means the object will keep doing what it has been doing – either continue moving at a constant velocity, or remaining at rest When the total positive and negative acceleration equals zero – cancels each other out If there is an acceleration then a force is acting on an object changing it motion.
- #6 Discuss the relationship between graphs. Constant velocity (flat, horizontal line) = zero acceleration Constant velocity (flat, horizontal line) means it will keep moving at the same speed How does this apply to Newtons’ Laws?
- #7 Discuss the relationship between graphs. Negative velocity means it is moving backwards – downward slope. Negative velocity means reverse motion. Constant velocity (flat, horizontal line) means no acceleration although it is still moving. How does this apply to Newton’s Laws?
- #8 Speeding up Positive, Constant acceleration Position line is curved because velocity is changing (Increasing speed) Speed is not constant – it is moving faster and faster each second but with a constant acceleration so the velocity line has a straight slope Because there is an acceleration – a change in motion – there is a net force acting on the object
- #9 Slowing down Constant, negative acceleration Position line is curved because velocity is changing (decreasing speed) Speed is not constant – it is moving slower and slower each second but with a constant, negative acceleration so the velocity line has a straight slope Because there is an acceleration - a change in motion – there is a net force acting on the object, only this time the force is in the opposite direction
- #10 1. Distance 2. Moves forward slowly (1), then faster (2), then backwards (3-4), then forward again much faster (4-7), then slower (7-8), then backwards again (8-10) – since all line segments are straight, all velocity is constant 3. Not according to this graph 0-1 4-7 Each section has a constant velocity because the position is changing at a steady rate – Any straight line is constant velocity The object is accelerating each time the velocity changes, and the acceleration is constantly changing
- #11 Speed (velocity) C-D Constant velocity – moving forward at a constant speed Stopped (at rest) A-B, C-D, E-F O-A, B-C, D-E = force, all others = no net force O-A moving forward, curving upward, A-B moving forward, constant slope, B-C moving forward at slower speed and curving down, C-D stopped – no movement, D-E moving forward again slower speed than before, E-F moving forward, steady slope – this object never goes backwards O-A positive acceleration, A-B, no acceleration, B-C negative, C-D none, D-E positive, E-F none
- #12 2-3 At the end (6-7) Positive (forward) – just at a slower velocity It doesn’t Positive – it never goes backwards because there is never a net negative acceleration Zero – because the sum of the positive forces is equal to the sum of the negative ones Moving forward with an upwards curve (0-2), then continues forward with a steady slope (2-4), then still moves forward but with a downwards curve (4-6), then it stops (straight line) Steady increase in velocity – steady slope up (0-2), then straight line, constant velocity (2-4), then decrease in velocity – steady slope down (4-6), the stopped