1. Physics 218 Lecture 3
Dr. David Toback
Physics 218, Lecture III

2. Quiz How many math quizzes have you finished?
When is Chapter 1 HW due?
When are you going to do Lab 2?
Name
Section
UIN
Physics 218, Lecture III

3. Checklist for Today Things that were due last Thursday:
Chapter 1 reading
Read all handouts from web page
Things that are due yesterday (Monday):
WebCT warm-ups (FCI, Math Assess, etc…)
Math Quizzes 1 through 10
Things that are due today:
Reading for Chapter 2
For this week and/or due next Monday:
Recitation: Read Lab 2 (on web), start Ch. 1 on WebCT
All HW1 problems on WebCT due Monday
Physics 218, Lecture III

4. Chapter 2: Motion in 1-Dimension
Position
Velocity
Acceleration
Problem Solving
Tricks
Methods
Examples
Physics 218, Lecture III

5. Physics 218, Lecture III

6. Describing Motion Interested in two key ideas:
How objects move as a function of time
Kinematics
Chapters 2, 3 and 4
Why objects move the way they do
Dynamics
Do this in Chapters 5 and 6
Physics 218, Lecture III

7. Notes before we begin
This chapter is a good example of a set of material that is best learned by doing examples
We’ll do some examples today
Lots more next time…
Physics 218, Lecture III

8. Equations of Motion We want Equations that describe
Where am I as a function of time?
How fast am I moving as a function of time?
What direction am I moving as a function of time?
Is its velocity changing? Etc.
Physics 218, Lecture III

9. Moving Car The example from last time: X = ct2
What’s the velocity at t=1 sec?
Physics 218, Lecture III

10. Check: Non-Constant Velocity
X = ct2 with c=11 ft/sec2
V = dX/dt = 2ct
The velocity is:
“non-Constant”
a “function of time”
“Changes with time”
V=0 ft/s at t0=0 sec
V=22 ft/s at t1=1 sec
V=44 ft/s at t2=2 sec
Physics 218, Lecture III

11. Acceleration If your velocity is changing, you are “accelerating”
You hit the accelerator in your car to speed up at a stop light
(Ok…It’s true you also hit it to stay at constant velocity, but that’s because friction is slowing you down…we’ll get to that later…)
How quickly is the velocity changing? That’s our Acceleration
Physics 218, Lecture III

12. Acceleration Acceleration is the “Rate of change of velocity”
Said differently: “How fast is the Velocity changing?” “What is the change in velocity as a function of time?”
Physics 218, Lecture III

13. Position, Velocity and Acceleration
All three are related
Velocity is the derivative of position with respect to time
Acceleration is the derivative of velocity with respect to time
Acceleration is the second derivative of position with respect to time
Calculus is REALLY important
Derivatives are something we’ll come back to over and over again
Physics 218, Lecture III

14. Important Equations of Motion
If the acceleration is constant
Position, velocity and Acceleration are vectors. More on this in Chap 3
Physics 218, Lecture III

15. Example You have an equation of motion where: X = X0 + V0t + ½at2
where X0, V0 , and a are constants.
What is the velocity and the acceleration?
 V = dx/dt = 0 + V0 + at
Remember that the derivative of a constant is Zero!!
 Accel = dV/dt =d2x/dt2 = a
Physics 218, Lecture III

16. constant acceleration:
Show that for
constant acceleration:
Physics 218, Lecture III

17. If the acceleration is zero, does that mean that the velocity is zero?
Conceptual Example
If the velocity of an object is zero, does it mean that the acceleration is zero?
If the acceleration is zero, does that mean that the velocity is zero?
Physics 218, Lecture III

18. Problem Solving Overview
There are good general problem solving TRICKS
Units checking
Special case checking
Etc.
There are good METHODS of problem solving that prepare you for the exams
We’ll use both to solve
problems in lecture
Physics 218, Lecture III

19. First Things First! Trick #1
What’s the first thing you should do when you’re given a a problem?
Draw a diagram!!!
Usually good for some partial credit
List givens and wants as variables
Also a good bet for partial credit
Then use reasonable equations and solve with your variables
Trick #1
Physics 218, Lecture III

20. Trick #2: Units
The speed of your car isn’t measured in seconds, its measured in meters/second (or miles/hour etc.)
Paying attention to the units will help you catch LOTS of mistakes on exams, quizzes and homework!!
If we ask what the mass of your car is, make sure your answer is in kg (or lbs etc.)
Trick #2: Every time you finish a problem ALWAYS check the units of your answer!!
Physics 218, Lecture III

21. Tricks #3 and #4 Check Reasonableness:
Can you find another way to do the same problem that gives the same answer?
Simple numbers give expected numerical answers? Example: Zero, or infinity
Trick #3
Trick #4
Physics 218, Lecture III

22. How to use the Tricks and Methods
Next we’ll do an example problem like one of the homework problems in the text book
Solve this problem using the right method
Draw a diagram
Convert the numbers to variables
Solve to get a formula
Plug in the numbers at the end
Check
Reasonable numbers?
Silly numbers?
Another way to do the same problem?
Physics 218, Lecture III

23. Car Crash Test Design
You are designing a crash test setup for a car maker. You can accelerate a car from rest with a constant acceleration of 1.00 m/s2 so you can make the car crash into a wall. (This is the last time you will see numbers in a problem in lecture).
If the path is 200m long, what is the velocity of the car just before/as it hits the wall?
For the same acceleration, if you want the car to hit the wall with a speed of 30m/s (about 60 mi/hr), what minimum length must you have?
Physics 218, Lecture III

24. How quickly can you stop a car?
You’re driving along a road at some constant speed, V0, and slam on the breaks and slow down with constant deceleration a.
How much time does it take to stop?
How far do you travel before you come to a stop?
Where you stop
When you hit the brakes
Physics 218, Lecture III

25. Free Fall Free fall is a good example for one dimensional problems
Gravity
Things accelerate towards earth with a constant acceleration I.e., a=g=9.8m/s2 towards the earth
We’ll come back to Gravity a lot!
Physics 218, Lecture III

26. Throw a Ball up
You throw a ball upward into the air with initial velocity V0. Calculate:
The time it takes to reach its highest point (the top).
Distance from your hand to the top
Time to go from your hand and come back to your hand
Velocity when it reaches your hand
Time from leaving your hand to reach some random height h.
Physics 218, Lecture III

27. Speeder X Police Officer Speeder
A speeder passes you (a police officer) sitting by the side of the road and maintains their constant velocity V. You immediately start to move after the speeder from rest with constant acceleration a.
How much time does it take to ram the speeder?
How far do you have to travel to catch the speeder?
What is your final speed? X
Police Officer Speeder
Physics 218, Lecture III

28. Results of Math Quizzes
The average of all Math Quizzes taken so far (not the Math Assessment) is about an 8.1 with a standard deviation of just above 1.1.
How to evaluate where you stand. If the average of the scores of all the quizzes you have taken is:
95% or above: Well prepared
85% - 90%: Good, but needs to be better
80% – 85%: Ok, but really needs some work
75% - 80%: Hmmmm…maybe get some help
75% or below: Careful…Definitely get help! Maybe drop…
Physics 218, Lecture III

29. Next Week
Reading and Lecture: Chapters 3 and 4, Vectors and Two Dimensional Motion
Recitation and WebCT Homework:
HW: HW1 due Monday
Recitation: Chapter 2
Recitation Prep: Do HW2 on paper, start turning in on WebCT before recitation
Lab: No lab next week
Physics 218, Lecture III

30. End of Lecture Notes
Physics 218, Lecture III

31. Our Example with Const. Acceleration
Physics 218, Lecture III

32. Decelerating Car
You are driving a car along a straight highway when you put on the brakes. The initial velocity is 15.0m/s to the right, and it takes 5.0s to slow the car down until it is moving at 5.0m/s to the right.
What is the car’s average acceleration?
Physics 218, Lecture III

33. Examples Can a car have uniform speed and non-constant velocity?
Can an object have a positive average velocity over the last hour, and a negative instantaneous velocity?
Physics 218, Lecture III

34. Constant Velocity This example: X = bt Slope is constant
Velocity is constant
Easy to calculate
Same everywhere
Physics 218, Lecture III

35. More Questions on the Car Crash
What is the distance traveled?
What is the total displacement?
What is the average speed?
Is the average speed the same as the average velocity?
What is the instantaneous velocity at all times?
Physics 218, Lecture III

36. Reference Frames Need to refer to some place as the origin
Frame of reference:
Need to refer to some place as the origin
Draw a coordinate axis
We define everything from here
Always draw a diagram!!!
Physics 218, Lecture III

37. If the motion started here, call this x0
Displacement
Where are you? I.e, What is your displacement?
Well…relative to where? Example: I’m 10 blocks north east of Kyle field
What do we need to know?
Where does the motion start? x0?
x0 is relative to the origin
x0 meters from the origin
When does the motion start? t0?
If the motion started here, call this x0
Physics 218, Lecture III

38. Scalar Distance traveled is 100m
Vectors vs. Scalars
Let’s say we traveled on a path like in the figure
Distance traveled from the origin is a Scalar (like your car odometer).
Displacement from the origin is a Vector
Has a distance and a direction from the origin
Speed is a scalar
Velocity is a vector
Negative distance?
Displacement?
Scalar Distance traveled is 100m
Vector Displacement
is 40m East
Physics 218, Lecture III

39. Another reason to care about vectors
It turns out that nature has decided that the directions don’t really care about each other.
Example: You have a position in X, Y and Z. If you have a non-zero velocity in only the Y direction, then only your Y position changes. The X and Z directions could care less. (I.e., they don’t change).
Represent these ideas with Vectors
Physics 218, Lecture III

40. Acceleration
An object is accelerating if it’s “velocity is changing as a function of time”
Acceleration = dv/dt
Acceleration and velocity can be pointing in different directions
How?
What is the difference between average acceleration and instantaneous acceleration?
Physics 218, Lecture III

41. If the motion started here, call this x0
Displacement
Where are you? I.e, What is your displacement?
Well…relative to where? Example: I’m 10 blocks north east of Kyle field
What do we need to know?
Where does the motion start? x0?
x0 is relative to the origin
x0 meters from the origin
When does the motion start? t0?
If the motion started here, call this x0
Physics 218, Lecture III

42. Average Velocity Average speed Average velocity Avg Speed = 100m/10s
Total time = 10sec
Avg Speed = 100m/10s
= 10m/s
Avg Velocity = (40m East)/10s
= 4m/s East
Physics 218, Lecture III

43. Instantaneous Velocity
Average and Instantaneous Velocity
Average is “over a period of time”
I.e., How many miles you traveled in a day
Instantaneous is how fast are you going “right now”
Car example:
Instantaneous is more like your speedometer.
Average is taking how far you traveled in the last hour and and dividing by an hour (includes the stops at the gas station)
Physics 218, Lecture III

44. Instantaneous Cont… V=Dx/Dt (use total change in x, t: average)
Magnitude of instantaneous velocity is always the same as the instantaneous speed
Why? In the last example, is the average velocity the same as the average speed?
Distance and displacement become identical in the limit that they become infinitesimally small
Physics 218, Lecture III

45. Calculus 1 Why are we doing math in a Physics class?
Believe it or not, Calculus and Classical mechanics were developed around the same time, and they essentially enabled each other.
Calculus basically IS classical mechanics
Bottom line: If you can’t do Calculus you can’t REALLY do physics.
It’s true you can do some simple problems
Physics 218, Lecture III

46. Advice You really need to be comfortable differentiating!
If you aren’t, do lots of problems in a introductory calculus book and take lots of math quizzes
The “rate” at which things “change” will be really big in everything we do
If you are struggling with the problems in the handout get help now
This stuff is going to go by quickly!
Physics 218, Lecture III

47. Overview I’m not going to teach you calculus The goals are:
Teach (hopefully remind) you about how to think about how things “change as a function of time”
Teach you how to take a derivative (and why you take derivatives) so you can get by until you get to it in your calculus class
Diagrams are vital again!
Units here will really help (there is a good example of this in problem 1-9 on the Calculus handout).
Physics 218, Lecture III

48. Some Notation Let’s do some definitions Define “define”
Example: t0  0 sec
We can always make a definition, the idea is to make one that is “useful”
Another example: X = 22 meters  X0
Define D as “the change in”
Physics 218, Lecture III