2. Using Graphs and Equations to Describe Motion Position-Time Graphs, Velocity-Time Graphs Position-Time Graphs, Velocity-Time Graphs

3. How can we calculate velocity?  Equation: Units:

4. How can we use position-time graphs to describe motion? 543210543210 Position (m) 0 5 10 15 20 25 Time (s)

5. Summary: Position-time graphs  Position - read y value at time t  Displacement - subtract positions  Distance - add legs  Velocity - slope  Position - read y value at time t  Displacement - subtract positions  Distance - add legs  Velocity - slope

6. How can we use velocity-time graphs to describe motion? 50 40 30 20 10 0 Velocity (m/s) 0 5 10 15 20 25 Time (s)

7. Summary: Velocity-time graphs  Instantaneous velocity - read y value at time t  Average velocity - add velocities and divide by 2  Distance/Displacement - area under the line  Acceleration - slope  Instantaneous velocity - read y value at time t  Average velocity - add velocities and divide by 2  Distance/Displacement - area under the line  Acceleration - slope

8. Formulas for Accelerating Objects:  Finding average velocity (two formulas): (already know this one) (we know this one, too, but it is not in the reference table!)

9. Formulas for Accelerating Objects:  Finding acceleration:

10. Formulas for Accelerating Objects:  Finding final velocity given constant acceleration: Wow! Looks like y = mx + b

11. Formulas for Accelerating Objects:  Finding displacement of an acceleration object: (two formulas): What does this look like on a graph?

12. Free Fall  Is gravity the same everywhere?  NO  Shape of the Earth - oblate spheroid  Sketch:  Gravity smaller at higher altitudes and at equator (greater distance to the center of the Earth)  Is gravity the same everywhere?  NO  Shape of the Earth - oblate spheroid  Sketch:  Gravity smaller at higher altitudes and at equator (greater distance to the center of the Earth)

13. How does velocity change as a ball is thrown in the air and allowed to fall?  Graphs:

14. Example:  A ball is thrown in the air. As it leaves your hand, it is traveling upward at 20 m/s.  Describe how the velocity changes as the ball rises and falls:  A ball is thrown in the air. As it leaves your hand, it is traveling upward at 20 m/s.  Describe how the velocity changes as the ball rises and falls:

15.  At what time will the velocity be 0 m/s?

16.  How high does the ball go?

17.  What is the displacement of the ball?