Acceleration

1. Acceleration 2.2 pp. 48-59 Mr. Richter

2. Agenda • Warm-Up • Introduction to Acceleration • Notes: • What is Acceleration? • Calculating Acceleration • Graphs of Acceleration • Review Homework Problems • Practice Acceleration Graphs

3. Agenda Day 2 and 3 Friday Monday Acceleration and Data Lab • More with • Kinematic Equations • Practice Problem Solving

4. Objectives: We Will Be Able To… • Describe motion in terms of changing velocity. • Compare graphical representations of accelerated and non-accelerated motions. • Apply kinematic equations to calculate distance, time or velocity under conditions of constant acceleration.

5. Warm-Up: • To the right is a Velocity vs. Time (VvT) graph of an object that starts at the origin. • Describe the motion of the object in one complete sentence. • Sketch the Position vs. Time graph you think describes the object Velocity Time

6. Warm Up Velocity vs. Time Position vs. Time Velocity Position Time Time

7. Acceleration

8. What is Acceleration? • What comes to mind when I say the word acceleration? • Discuss at your tables for 1 minute and then we will discuss as a class.

9. What is Acceleration? • Most objects do not travel at a constant speed all of the time. • Acceleration is the rate of change of velocity. • In other words: • how quickly does velocity change • how long does it take to change from one velocity or another • how quickly an object speeds up or slows down • As well as: how quickly an object changes direction. More on this in later topics.

10. What is Accleration? • Just like displacement and velocity, acceleration has direction and magnitude (size, amount). • We consider: • acceleration to the right or up to be positive, and • to the left or down to be negative. • NOTE: An object does not have to be moving in the positive direction (positive velocity) to have positive acceleration, or vice versa. • It only needs to be “trending” toward positive velocity.

11. Calculating Acceleration Formula Time!

12. Calculating Acceleration: Formula • Acceleration is the rate of change in velocity, or how much velocity changes with time.

13. Calculating Acceleration: Units • If acceleration is the rate of change in velocity [m/s] relative to time [s]… • The units for acceleration are(often): • We abbreviate this verbally as “meters per second squared”. • But we really mean “meters per second per second”, or a change in meters per second (velocity) every second (time). • Therefore, 5 m/s2 really means a 5 m/s change in velocity every second.

14. Practice Problem • A shuttle bus slows to a astop with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to 0.0 m/s? • Δt = 5.0 sec

15. Graphs of Acceleration Velocity vs. Time

16. Velocity vs. Time (VvT) Graphs • Position vs. Time graphs show us the velocity of an object. • Similarly, Velocity vs. Time graphs show us the acceleration of an object. • In your notes, sketch what you think the VvT graph looks like for (2 mins): • Positive Acceleration • Negative Acceleration • No Acceleration

17. Velocity vs. Time Graphs Velocity Velocity Velocity Time Time Time Positive Acceleration Positive Slope Negative Acceleration Negative Slope Zero Acceleration Zero Slope

18. VvT and PvT Graphs Together How does positive acceleration affect position? Velocity Position Time Time

19. VvT and PvT Graphs Together How does positive acceleration affect position? Velocity Position Time Time

20. VvT and PvT Graphs Together How does positive acceleration affect position? Velocity Position Time Time

21. VvT and PvT Graphs Together • What do the position graphs look like for the 3 possibilities for negative acceleration? Sketch them in your notes. Velocity Velocity Velocity Time Time Time

22. VvT and PvT Graphs Together • What do the position graphs look like for the 3 possibilities for negative acceleration? Sketch them in your notes. Position Position Position Time Time Time

23. VvT and PvT Graphs Together • What about zero acceleration? • Zero acceleration = no change in velocity… • Constant velocity! • You already know what this looks like! Velocity Position Time Time

24. VvT and PvT Graphs Together • To Summarize: (p. 51)

25. Homework • Due tomorrow: p. 49 #3-5

26. Motion with Constant Acceleration Get ready for formulas.

27. A note about Constant Acceleration Formulas • All of the following are derived from either the definition of velocity or the definition of acceleration. • Derivations are in your book on pp. 52-56. • They’re not magic, but we don’t really have the time to get into where they come from. • We will only deal with constant acceleration in this class. More advanced physics classes discuss changes in acceleration as well.

28. Displacement with Constant Uniform Acceleration • The amount of displacement an object experiences depends on: • the initial velocity (how fast are you going when you start) • the acceleration (how quickly do you change that velocity) • time (how do you move while you’re changing the velocity)

29. Velocity with Constant Uniform Acceleration • The final velocity depends on: • the initial velocity (how fast are you going at the start) • the acceleration (how quickly do you change that velocity) • the time (how long do you change that velocity)

30. Displacement with Constant Uniform Acceleration • Combine the last two formulas and simplify…

31. Final Velocity after any Displacement • Another combination…

32. All Four Together (p.58) • Note the difference between the right and left column. • All formulas contain some information but omit others. • This is your toolbox. Each problem you solve require you to use one or more tools. You choose.

33. Practice Problem • a. 16 m/s • b. 7.0 s

34. Wrap-Up: Did we meet our objectives?