1. Learning Goals Draw displacement-time graphs, and use the graphs to calculate average velocity and instantaneous velocity of moving objects in one dimension Distinguish between constant, instantaneous, and average speed, and give examples of each involving uniform and non-uniform motion

2. Position-time Graphs

3. Position-Time Graphs Position-Time graphs: a graph describing the motion of an object, with position on the vertical axis and time on the horizontal axis

4. Creating a Position Time Graph A soccer ball is kicked east of a soccer player. The following data shows the position of the soccer ball relative to the player over a period of 6 seconds. Create a position time graph. 00 14 28 312 416 520 624

5. Position-time graphs From the graph that you created how do you think we could find the velocity of the soccer ball? The slope of a position-time graph gives us the average velocity of the object Reminder: slope = rise/run m = (d  2 - d  1 )/(t 2 - t 1 ) m =  d  /  t v  av =  d  /  t

6. Creating a Position Time Graph The next slide shows data of a person leaving their house and walking to the corner store. Create a position-time graph from the data.

7. 00 12 24 36 48 58 68 710 813 917 1022

8. Average Velocity and Instantaneous Velocity We said earlier that you can calculate the average velocity from a position time graph by calculating the slope Calculate the average velocity for the following time intervals: a)0 to 3 seconds b)4 to 6 seconds c)6 to 10 seconds d)0 to 10 seconds

9. Average Velocity and Instantaneous Velocity

10. 0t(s) d  (m[E]) Tangent Lines Run Rise Use this process to find the instantaneous velocity at 9 seconds on your position-time graph for the person walking to the corner store

11. Let’s take a look at the motion of a student using the motion sensor

12. 0t(s) d  (m[E]) Analyzing Position-time graphs Describe the motion that is shown in the graph.

13. 0t(s) d  (m[E]) Analyzing Position-time graphs Describe the motion that is shown in the graph.

14. 0t(s) d  (m[E]) Analyzing Position-time graphs Describe the motion that is shown in the graph.

15. 0t(s) d  (m[E]) Analyzing Position-time graphs Describe the motion that is shown in the graph.

16. 0t(s) d  (m[E]) Analyzing Position-time graphs Describe the motion that is shown in the graph.

17. 0t(s) d  (m[E]) Analyzing Position-time graphs Describe the motion that is shown in the graph. Does anyone know what this type of motion is called?

18. Uniform and Non-uniform Velocity Uniform or constant velocity: moving at a constant speed in a straight line ex. A car travels down a straight highway at a steady 100km/h

19. 0t(s) d  (m[E]) Constant Velocity Describe the motion that is shown in the graph.

20. Uniform and Non-uniform Velocity Non-uniform velocity: motion in which the object’s speed changes or the object does not travel in a straight line ex1. A parachutist jumps out of an aircraft. (before the parachute opens) What happens after the parachute opens? ex2. A passenger on an amusement park ride travels in a circle at a constant speed of 1.2m/s.

21. 0t(s) d  (m[E]) Describe the motion that is shown in the graph. Does anyone know what this type of motion is called? Non-uniform Velocity

22. Assignment You will be creating a position-time graph for the motion of a dynamics cart rolling down a ramp You will use your ticker-tape timer to collect data and create a data chart From your data chart you will create a position- time graph Make sure you give your graph a title and label both the axis. Your data table should also have a title. After completing your graph determine whether the motion is demonstrating uniform or non- uniform velocity