1. Welcome to Physics C Instructor:
Physics C 1-D Motion
Welcome to Physics C
Instructor:
Dr. Peggy Bertrand
x 2568
Expectations are on the Course Description page.
Homework assignments are on the course calendar.
Write your name inside the front cover of your textbook.
Add (Bertrand) on the same line with your name.
Bring your lab fee of $15 to me beginning tomorrow. Due Friday.
Bertrand

2. Physics C 1-D Motion
Information Card
Bertrand

3. Philosophy of Instruction for Physics C
Physics C 1-D Motion
Philosophy of Instruction for Physics C
You are the big kids.
You have all had physics before.
Your motivations for being in this course vary.
Your skill and interest level in different areas of physics vary.
I will try to avoid repetition of what you already know, and will occasionally give you at least some choice as to what you work on.
Bertrand

4. Physics C 1-D Motion Average Speed, Velocity, Acceleration
August 18, 2008
Average Speed, Velocity, Acceleration
Bertrand

5. Average Speed and Average Velocity
Physics C 1-D Motion
Average Speed and Average Velocity
Average speed describes how fast a particle is moving. It is calculated by:
Average velocity describes how fast the displacement is changing with respect to time:
always positive
sign gives direction
Bertrand

6. Physics C 1-D Motion
Average Acceleration
Average acceleration describes how fast the velocity is changing with respect to time. The equation is:
sign determines direction
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7. Physics C 1-D Motion
Sample problem: A motorist drives north at 20 m/s for 20 km and then continues north at 30 m/s for another 20 km. What is his average velocity?
Bertrand

8. Physics C 1-D Motion
Sample problem: It takes the motorist one minute to change his speed from 20 m/s to 30 m/s. What is his average acceleration?
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9. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph A B x Dx Dt t
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10. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph A B t x Dx Dt
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11. Average Acceleration from a Graph
Physics C 1-D Motion
Average Acceleration from a Graph A B v Dx Dt t
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12. Sample problem: From the graph, determine the average velocity for the particle as it moves from point A to point B.
Physics C 1-D Motion -1 -2 1 2
0.1
0.2
0.3
0.4
0.5 -3 3
t(s)
x(m) A B
Bertrand

13. Sample problem: From the graph, determine the average speed for the particle as it moves from point A to point B.
Physics C 1-D Motion -1 -2 1 2
0.1
0.2
0.3
0.4
0.5 -3 3
t(s)
x(m) A B
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14. Physics C 1-D Motion Instantaneous Speed, Velocity, and Acceleration
August 19, 2008
Instantaneous Speed, Velocity, and Acceleration
Bertrand

15. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph A t x B
Remember that the average velocity between the time at A and the time at B is the slope of the connecting line.
Bertrand

16. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph A t x B
What happens if A and B become closer to each other?
Bertrand

17. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph t x A B
What happens if A and B become closer to each other?
Bertrand

18. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph t x B A
What happens if A and B become closer to each other?
Bertrand

19. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph t x B A
What happens if A and B become closer to each other?
Bertrand

20. Average Velocity from a Graph
Physics C 1-D Motion
Average Velocity from a Graph t x
A and B are effectively the same point. The time difference is effectively zero. B A
The line “connecting” A and B is a tangent line to the curve. The velocity at that instant of time is represented by the slope of this tangent line.
Bertrand

21. Sample problem: From the graph, determine the instantaneous speed and instantaneous velocity for the particle at point B.
Physics C 1-D Motion -1 -2 1 2
0.1
0.2
0.3
0.4
0.5 -3 3
t(s)
x(m) A B
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22. Average and Instantaneous Acceleration
Physics C 1-D Motion
Average and Instantaneous Acceleration t v
Instantaneous acceleration is represented by the slope of a tangent to the curve on a v/t graph. A
Average acceleration is represented by the slope of a line connecting two points on a v/t graph. C B
Bertrand

23. Average and Instantaneous Acceleration
Physics C 1-D Motion
Average and Instantaneous Acceleration
Instantaneous acceleration is zero where slope is constant x
Instantaneous acceleration is positive where curve is concave up
Instantaneous acceleration is negative where curve is concave down t
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24. Physics C 1-D Motion
Sample problem: Consider an object that is dropped from rest and reaches terminal velocity during its fall. What would the v vs t graph look like? t v
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25. Physics C 1-D Motion
Sample problem: Consider an object that is dropped from rest and reaches terminal velocity during its fall. What would the x vs t graph look like? t x
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26. Estimate the net change in velocity from 0 s to 4.0 s
Physics C 1-D Motion
Estimate the net change in velocity from 0 s to 4.0 s
a (m/s2)
1.0
t (s)
2.0
4.0
-1.0
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27. Estimate the net displacement from 0 s to 4.0 s
Physics C 1-D Motion
Estimate the net displacement from 0 s to 4.0 s
v (m/s)
2.0
t (s)
4.0
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28. Physics C 1-D Motion Derivatives
August 20, 2008
Derivatives
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29. Announcements Remember to pay lab fee by Friday.
Physics C 1-D Motion
Announcements
Remember to pay lab fee by Friday.
Homework quiz tomorrow.
Remember to check web site calendar for homework.
Bertrand

30. Sample problem. From this position-time graph
Physics C 1-D Motion
Sample problem. From this position-time graph x t
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31. Draw the corresponding velocity-time graph
Physics C 1-D Motion
Draw the corresponding velocity-time graph x t
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32. Suppose we need instantaneous velocity, but don’t have a graph?
Physics C 1-D Motion
Suppose we need instantaneous velocity, but don’t have a graph?
Suppose instead, we have a function for the motion of the particle.
Suppose the particle follows motion described by something like
x = (-4 + 3t) m
x = ( t – ½ 3 t2) m
x = -12t3
We could graph the function and take tangent lines to determine the velocity at various points, or…
We can use differential calculus.
Bertrand

33. Instantaneous Velocity
Physics C 1-D Motion
Instantaneous Velocity
Mathematically, velocity is referred to as the derivative of position with respect to time.
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34. Instantaneous Acceleration
Physics C 1-D Motion
Instantaneous Acceleration
Mathematically, acceleration is referred to as the derivative of velocity with respect to time
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35. Instantaneous Acceleration
Physics C 1-D Motion
Instantaneous Acceleration
Acceleration can also be referred to as the second derivative of position with respect to time.
Just don’t let the new notation scare you; think of the d as a baby D, indicating a very tiny change!
Bertrand

36. Evaluating Polynomial Derivatives
Physics C 1-D Motion
Evaluating Polynomial Derivatives
It’s actually pretty easy to take a derivative of a polynomial function. Let’s consider a general function for position, dependent on time.
Bertrand

37. Physics C 1-D Motion
Sample problem: A particle travels from A to B following the function x(t) = 3.0 – 6t + 3t2.
What are the functions for velocity and acceleration as a function of time?
What is the instantaneous velocity at 6 seconds?
What is the initial velocity?
Bertrand

38. Physics C 1-D Motion
Sample problem: A particle travels from A to B following the function x(t) = 2.0 – 4t + 3t2 – t3.
What are the functions for velocity and acceleration as a function of time?
What is the instantaneous acceleration at 6 seconds?
Bertrand

39. Sample problem: A particle follows the function
Physics C 1-D Motion
Sample problem: A particle follows the function
Find the velocity and acceleration functions.
Find the instantaneous velocity and acceleration at 2.0 seconds.
Bertrand

40. Physics C 1-D Motion Kinematic Graphs -- Laboratory
August 21, 2008
Kinematic Graphs -- Laboratory
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41. Physics C 1-D Motion
Announcements
The packet I gave you yesterday is due on Friday. Whenever I give you a packet, it will be turned in for a grade.
Remember to pay lab fee by tomorrow. I’ll collect today during the lab.
Get out one sheet of paper, pencil, and calculator for the homework quiz. Put your name, date, and period number at the top.
Let’s roll the die…
Bertrand

42. Kinematic Graphs Laboratory
Physics C 1-D Motion
Kinematic Graphs Laboratory
Purpose: to use a motion sensor to collect graphs of position-versus-time and velocity-versus-time for an accelerating object, and to use these graphs to clearly show the following:
That the slopes of tangent lines to the position versus time curve yield instantaneous velocity values at the corresponding times.
That the area under the curve of a velocity versus time graph yields displacement during that time period.
Experiments: You’ll do two experiments. The first must involve constant non-zero acceleration. You can use the cart tracks for this one. The second must involve an object that is accelerating with non-constant non-zero acceleration. Each experiment must have a position-versus-time and velocity-versus-time graph that will be analyzed as shown above.
Report: A partial lab report in your lab notebook must be done. The report will show a sketch of your experimental apparatus. Computer-generated graphs of position versus time and velocity versus time must be taped into your lab notebook. An analysis of the graphical data must be provided that clearly addresses A and B above, and a brief conclusion must be written.
Bertrand

43. Setting up your Lab Book
Physics C 1-D Motion
Setting up your Lab Book
Put your name inside the front cover. Write it on the bottom on the white page edges.
For each lab:
Record title at top where indicated
Record lab partners and date at bottom.
Record purpose under title.
List equipment.
Note computer number, if relevant
For these labs, you will insert printouts of graphs in your lab books, and do the analysis on the graphs and in the book.
Bertrand

44. Physics C 1-D Motion Kinematic Equation Review
August 25, 2008
Kinematic Equation Review
Bertrand

45. Physics C 1-D Motion
Announcements
Friday’s lab report is due Wednesday. If you missed the lab, come by during the morning to make it up.
Bertrand

46. Here are our old friends, the kinematic equations 
Physics C 1-D Motion
Here are our old friends, the kinematic equations 
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47. Physics C 1-D Motion
Sample problem (basic): Show how to derive the 1st kinematic equation from the 2nd.
Sample problem (advanced): Given a constant acceleration of a, derive the first two kinematic equations.
Bertrand

48. Draw representative graphs for a particle which is stationary.
Physics C 1-D Motion
Draw representative graphs for a particle which is stationary. x t
Position vs
time v t
Velocity vs
time a t
Acceleration vs
time
Bertrand

49. Physics C 1-D Motion
Draw representative graphs for a particle which has constant non-zero velocity. x t
Position vs
time v t
Velocity vs
time a t
Acceleration vs
time
Bertrand

50. Physics C 1-D Motion
Draw representative graphs for a particle which has constant non-zero acceleration. x t
Position vs
time v t
Velocity vs
time a t
Acceleration vs
time
Bertrand

51. Physics C 1-D Motion
Sample problem: A body moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x direction when its x coordinate is 3.0 cm. If the x coordinate 2.00 s later is cm, what is the magnitude of the acceleration?
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52. Physics C 1-D Motion
Sample problem: A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of m/s2 as it comes to a halt. a) What is the minimum time it needs after it touches down before it comes to a rest? b) Can this plane land at a small tropical island airport where the runway is km long?
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53. Air track demonstration
Physics C 1-D Motion
Air track demonstration
Kinematic graphs for uniformly accelerating object.
Curve-fit and equation comparison
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54. Physics C 1-D Motion Freefall
Tuesday, August 26, 2008
Freefall
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55. Announcements… Lab fees: Chris, Greg, Liam???
Physics C 1-D Motion
Announcements…
Lab fees: Chris, Greg, Liam???
Turn in your lab books tomorrow with:
Kinematics Graphing Lab
Bertrand

56. Physics C 1-D Motion
Free Fall
Free fall is a term we use to indicate that an object is falling under the influence of gravity, with gravity being the only force on the object.
Gravity accelerates the object toward the earth the entire time it rises, and the entire time it falls.
The acceleration due to gravity near the surface of the earth has a magnitude of 9.8 m/s2. The direction of this acceleration is DOWN.
Air resistance is ignored.
Bertrand

57. Physics C 1-D Motion
Sample problem: A student tosses her keys vertically to a friend in a window 4.0 m above. The keys are caught 1.50 seconds later. a) With what initial velocity were the keys tossed? b) What was the velocity of the keys just before they were caught?
Bertrand

58. Physics C 1-D Motion
Sample problem: A ball is thrown directly downward with an initial speed of 8.00 m/s from a height of 30.0 m. How many seconds later does the ball strike the ground?
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59. Physics C 1-D Motion
Picket Fence Lab
Use a laptop, Science Workshop 500, accessory photogate, and picket fence to determine the acceleration due to gravity. You must have position versus time and acceleration versus time data, which you will then fit to the appropriate function. Gravitational acceleration obtained in this experiment must be compared to the standard value of 9.81 m/s2.
Bertrand