1. Constant Velocity and Uniform Acceleration Teacher Excellence Workshop June 18, 2008

2. Distance  The total length of the path traveled by an object is called distance.  “How far have you walked?” is a typical distance question.  The SI unit of distance is the meter (m).  Distance is always positive. It has no direction. It is an example of a scalar.

3. Displacement (  x)  The change in the position of a particle is called displacement.  “How far are you from home?” is a typical displacement question.  The SI unit for displacement is the meter.  Displacement has a direction. In 1D motion, it can be positive or negative. It is an example of a vector.  Calculation of displacement:

4. A B Distance vs Displacement  Have your students draw the distance and displacement of a particle that moves from A to B around an oval track.

5. A B Distance vs Displacement  Have your students draw the distance and displacement of a particle that moves from A to B around an oval track.

6. Let’s Do a Lab!  Purpose: Figure out a way to make a cart move with an average velocity of as close to 0.200 m/s as possible. Use only the equipment provided. Photogate must be in PULSE mode.  Report: Write your BRIEF lab report. The section I want you to focus on in this lab report is the procedure section. Check my web site for examples of good procedures, and for the lab report guidelines.

7. Practice Problem: You drive in a straight line at 10 m/s for 1.0 km, and then you drive in a straight line at 20 m/s for another 1.0 km. What is your average velocity?

9. Qualitative Demonstrations 1)Demonstrate the motion of a particle that has an average speed and an average velocity that are both zero. 2)Demonstrate the motion of a particle that has an average speed and an average velocity that are both nonzero. 3)Demonstrate the motion of a particle that has an average speed that is nonzero and an average velocity that is zero. 4)Demonstrate the motion of a particle that has an average velocity that is nonzero and an average speed that is zero.

10. Quantitative Demonstration  You are a particle located at the origin. Demonstrate how you can move from x = 0 to x = 5.0 and back with an average speed of 0.5 m/s.  What the particle’s average velocity for the above demonstration?

11. Graphical Problem Demonstrate the motion of this particle. t x

12. Graphical Problem Demonstrate the motion of this particle. t x

13. Graphical Problem What physical feature of the graph gives the constant velocity from A to B? t x xx tt A B v ave =  x/  t

14. Graphical Review Problem Demonstrate the motion of these two particles. t x

15. Graphical Problem Demonstrate the motion of these two particle. t v

16. Graphical Problem t x What kind of motion does this graph represent?

17. Graphical Problem Can you determine average velocity from the time at point A to the time at point B from this graph? t x A B xx tt v ave =  x/  t

18. Graphical Problem: Determine the average velocity of this particle between 1 and 4 seconds. x (m)

19. Graphical Problem: Determine the average velocity from the graph. x (m)

20. Graphical Problem: Determine the average velocity between 1 and 4 seconds.

22. Instantaneous Velocity  The velocity at a single instant in time.  If the velocity is uniform, or constant, the instantaneous velocity is the same as the average velocity.  If the velocity is not constant, than the instantaneous velocity is not the same as the average velocity, and we must carefully distinguish between the two.

23. Instantaneous Velocity Draw a tangent line to the curve at B. The slope of this line gives the instantaneous velocity at that specific time. t x B xx tt v ins =  x/  t

24. Practice Problem: Determine the instantaneous velocity at 1.0 second.

26. Acceleration (a)  Any change in velocity over a period of time is called acceleration.  The sign (+ or -) of acceleration indicates its direction.  Acceleration can be…  speeding up  slowing down  turning

27. Questions  If acceleration is zero, what does this mean about the motion of an object?  Is it possible for a racecar circling a track to have zero acceleration?

28. Questions  If acceleration is zero, what does this mean about the motion of an object?  Ans: It is not changing.  Is it possible for a racecar circling a track to have zero acceleration?  Ans: Nope; the direction of the velocity is changing.

29. Uniform (Constant) Acceleration  In most high school physics courses, we will generally assume that acceleration is constant or uniform.  With this assumption we are free to use this equation:  The SI unit of acceleration is the m/s 2.

30. Acceleration in 1-D Motion has a sign!  The sign indicates direction. Acceleration is therefore a vector.  If the sign of the velocity and the sign of the acceleration is the same, the object speeds up.  If the sign of the velocity and the sign of the acceleration are different, the object slows down.

31. Qualitative Demonstrations 1)Demonstrate the motion of a particle that has zero initial velocity and positive acceleration. 2)Demonstrate the motion of a particle that has zero initial velocity and negative acceleration. 3)Demonstrate the motion of a particle that has positive initial velocity and negative acceleration. 4)Demonstrate the motion of a particle that has negative initial velocity and positive acceleration.

32. Practice Problem: A 747 airliner reaches its takeoff speed of 180 mph in 30 seconds. What is its average acceleration?

34. Practice Problem: A horse is running with an initial velocity of 11 m/s, and begins to accelerate at –1.81 m/s 2. How long does it take the horse to stop?

36. Graphical Problem Demonstrate the motion of this particle. Is it accelerating? t (s) v (m/s) 0.50

37. Graphical Problem Demonstrate the motion of this particle. Is it accelerating? t v

38. Graphical Problem What physical feature of the graph gives the acceleration? t v vv tt A B a =  v/  t

39. Practice Problem: Determine the acceleration from the graph.

41. Kinematic Equations for uniformly accelerating objects