Position Velocity Acceleration Graphs PRACTICE PROBLEMS SPS 8

Position, Velocity, Acceleration Graphs PRACTICE PROBLEMS SPS 8. Students will determine relationships among force, mass, and motion. a. Calculate velocity and acceleration.

Position Graphs 1. 2. 3. 4. 5. In which section(s) was the cart traveling at a constant positive velocity? In which section(s) was the cart traveling at a constant negative velocity? In which section(s) was the cart at rest? In which section did the cart maintain its greatest average speed? How fast was it traveling? How can you tell when the velocity is constant? How can you tell about an objects VELOCITY from a position graph?

Velocity Graphs 1. 2. 3. 4. 5. During which time interval(s) did it travel in a positive direction? During which time interval(s) did it travel in a negative direction? Describe the object’s movement between 10 and 15 minutes? What is the car’s acceleration between 10 and 15 minutes? 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?

Position vs. Velocity Graphs 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?

Acceleration Graphs 1. What does 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?

Constant Positive Velocity What is happening with 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).

Constant Negative Velocity What is happening with 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).

Positive Velocity with Positive Acceleration Is the object 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).

Positive Velocity and Negative Acceleration Is the object 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).

Graph Practice 1. What is 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?

Graph Practice 1. What is 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?

Graph Practice 1. Between what 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?

Assignments CARS IN GARAGE – CLASS ACTIVITY 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!) 1. 2.

Graphing Activity: Cars in Garage