1. College Physics, 7th Edition
Lecture
Chapter 2
College Physics, 7th Edition
Wilson / Buffa / Lou
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2. Chapter 2 Kinematics: Description of Motion
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3. Units of Chapter 2 Distance and Speed: Scalar Quantities
One-Dimensional Displacement and Velocity: Vector Quantities
Acceleration
Kinematic Equations (Constant Acceleration)
Free Fall
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4. Defining the important variables
Kinematics is a way of describing the motion of objects without describing the causes. You can describe an object’s motion:
In words Mathematically Pictorially Graphically
No matter HOW we describe the motion, there are several KEY VARIABLES that we use.
Symbol
Variable
Units t
Time s a
Acceleration
m/s/s
x or y
Displacement m vo
Initial velocity
m/s v
Final velocity
g or ag
Acceleration due to gravity

5. 2.1 Distance and Speed: Scalar Quantities
Distance is the path length traveled from one location to another. It will vary depending on the path.
Distance is a scalar quantity—it is described only by a magnitude.
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6. 2.1 Distance and Speed: Scalar Quantities
Average speed is the distance traveled divided by the elapsed time:
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7. 2.1 Distance and Speed: Scalar Quantities
Since distance is a scalar, speed is also a scalar (as is time).
Instantaneous speed is the speed measured over a very short time span. This is what a speedometer reads.
Scalar Example
Magnitude
Speed
20 m/s
Distance
10 m
Age
15 years
Heat
1000 calories
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8. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
A vector has both magnitude and direction. Manipulating vectors means defining a coordinate system, as shown in the diagrams to the left.
Right-hand Rule… first of many
Vector!!!
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9. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Displacement is a vector that points from the initial position to the final position of an object. Different from distance.
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10. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Note that an object’s position coordinate may be negative, while its velocity may be positive; the two are independent.
This can be VERY tricky for some students.
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11. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
For motion in a straight line with no reversals, the average speed and the average velocity are the same.
Otherwise, they are not.
The average velocity of a round trip is zero, as the total displacement is zero!
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12. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Different ways of visualizing uniform velocity:
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13. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
This object’s velocity is not uniform. Does it ever change direction, or is it just slowing down and speeding up?
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14. 2.2 One-Dimensional Displacement and Velocity: Vector Quantities
Magnitude & Direction
Velocity
20 m/s, N
Acceleration
10 m/s/s, E
Force
5 N, West
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15. 2.3 Acceleration
Acceleration is the rate at which velocity changes. Since velocity is a vector, so too is acceleration. Notice the bar over the a.
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16. 2.3 Acceleration
Acceleration means that the speed of an object is changing, or its direction is, or both. Ex B can be tricky.
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17. 2.3 Acceleration
Acceleration may result in an object either speeding up or slowing down (or simply changing its direction).
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18. 2.3 Acceleration
If the acceleration is constant, we can find the velocity as a function of time:
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19. 2.4 Kinematic Equations (Constant Acceleration)
From previous sections:
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20. 2.4 Kinematic Equations (Constant Acceleration)
Substitution gives:
and:
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21. 2.4 Kinematic Equations (Constant Acceleration)
These are all the equations we have derived for constant acceleration. The correct equation for a problem should be selected considering the information given and the desired result.
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22. 2.4 Kinematic Equations (Constant Acceleration)
These are all the equations we have derived for constant acceleration. The correct equation for a problem should be selected considering the information given and the desired result.
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23. Kinematic Example #1
Example: A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s/s.
a) How fast is the boat moving after accelerating for 5 seconds?
What do I know?
What do I want?
vo= 1.50 m/s
v = ?
a = 2.40 m/s/s
t = 5 s
13.5 m/s

24. Kinematic Example #2
b) How far did the boat travel during that time?
37.5 m

25. Does all this make sense?
13.5 m/s
1.5 m/s
Total displacement = = 37.5 m = Total AREA under the line.

26. Interesting to Note A = HB
Most of the time, xo=0, but if it is not don’t forget to ADD in the initial position of the object.
A=1/2HB

27. Kinematic Example #3
Example: You are driving through town at 12 m/s when suddenly a ball rolls out in front of your car. You apply the brakes and begin decelerating at 3.5 m/s/s.
How far do you travel before coming to a complete stop?
What do I know?
What do I want?
vo= 12 m/s
x = ?
a = -3.5 m/s/s
V = 0 m/s
20.57 m

28. 2.5 Free Fall
An object in free fall has a constant acceleration (in the absence of air resistance) due to the Earth’s gravity.
This acceleration is directed downward.
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29. 2.5 Free Fall
The effects of air resistance are particularly obvious when dropping a small, heavy object such as a rock, as well as a larger light one such as a feather or a piece of paper.
However, if the same objects are dropped in a vacuum, they fall with the same acceleration.
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30. 2.5 Free Fall
Here are the constant-acceleration equations for free fall:
**The positive y-direction has been chosen to be upwards. If it is chosen to be downwards, the sign of g would need to be changed.
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31. Examples
A stone is dropped at rest from the top of a cliff. It is observed to hit the ground 5.78 s later. How high is the cliff?
What do I know?
What do I want?
voy= 0 m/s
y = ?
g = -9.8 m/s2
yo=0 m
t = 5.78 s
Which variable is NOT given and
NOT asked for?
Final Velocity! m
H =163.7m

32. Examples
A pitcher throws a fastball with a velocity of 43.5 m/s. It is determined that during the windup and delivery the ball covers a displacement of 2.5 meters. This is from the point behind the body when the ball is at rest to the point of release. Calculate the acceleration during his throwing motion.
Which variable is NOT given and
NOT asked for?
What do I know?
What do I want?
vo= 0 m/s
a = ?
x = 2.5 m
v = 43.5 m/s
TIME
378.5 m/s/s

33. Examples
How long does it take a car at rest to cross a 35.0 m intersection after the light turns green, if the acceleration of the car is a constant 2.00 m/s/s?
What do I know?
What do I want?
vo= 0 m/s
t = ?
x = 35 m
a = 2.00 m/s/s
Which variable is NOT given and
NOT asked for?
Final Velocity
5.92 s

34. Examples
A car accelerates from 12.5 m/s to 25 m/s in 6.0 seconds. What was the acceleration?
What do I know?
What do I want?
vo= 12.5 m/s
a = ?
v = 25 m/s
t = 6s
Which variable is NOT given and
NOT asked for?
DISPLACEMENT
2.08 m/s/s

35. Graphical Analysis of Motion Very small section in your text
Graphical Analysis of Motion Very small section in your text. I am not happy with it so I have added the following…

36. Slope – A basic graph model
A basic model for understanding graphs in physics is SLOPE.
Using the model - Look at the formula for velocity.
Who gets to play the role of the slope?
Who gets to play the role of the y-axis or the rise?
Who get to play the role of the x-axis or the run? 
What does all the mean? It means that if your are given a graph, to find the velocity of an object during specific time intervals simply find the slope.
Velocity
Displacement
Time

37. Displacement vs. Time graph
What is the velocity of the object from 0 seconds to 3 seconds?
The velocity is the slope!

38. Displacement vs. Time graph
What is the velocity of the object from 7 seconds to 8 seconds?  Once again...find the slope!
A velocity of 0 m/s. What does this mean? It is simple....the object has simply stopped moving for 1 second.

39. Displacement vs. Time graph
What is the velocity from 8-10 seconds? You must remember to find the change it is final - initial.
The answer is negative! It is no surprise, because the slope is considered to be negative.
This value could mean several things:
The object could be traveling WEST or SOUTH. The object is going backwards - this being the more likely choice!
You should also understand that the slope does NOT change from 0-3s , 5 to 7s and 8- 10s.
This means that the object has a CONSTANT VELOCITY or IT IS NOT ACCELERATING.

40. Example
It is very important that you are able to look at a graph and explain it's motion in great detail. These graphs can be very conceptual.
Look at the time interval t = 0 to t = 9 seconds. What does the slope do?
It increases, the velocity is increasing
Look at the time interval t = 9 to t = 11 seconds. What does the slope do?
No slope. The velocity is ZERO.
Look at the time interval t = 11 to t = 15 seconds. What does the slope do?
The slope is constant and positive. The object is moving forwards at a constant velocity.
Look at the time interval t = 15 to t = 17 seconds. What does the slope do?
The slope is constant and negative. The object is moving backwards at a constant velocity.

41. Slope – A basic graph model
Let’s look at another model
Who gets to play the role of the slope for v-t graph?
Who gets to play the role of the y-axis or the rise?
Who get to play the role of the x-axis or the run? 
What does all the mean? It means that if your are given a Velocity vs. Time graph. To find the acceleration of an object during specific time intervals simply find the slope.
Acceleration
Velocity
Time

42. Velocity vs. Time Graph What is the acceleration from 0 to 6s?
You could say one of two things here: The object has a ZERO acceleration
The object has a CONSTANT velocity
What is the acceleration from 14 to 15s?
A negative acceleration is sometimes called DECELERATION. In other words, the object is slowing down. An object can also have a negative acceleration if it is falling. In that case the object is speeding up. CONFUSING? Be careful and make sure you understand WHY the negative sign is there.

43. Velocity vs. Time Graph
Conceptually speaking, what is the object doing during the time interval t = 9 to t = 13 seconds?
Does the steepness or slope increase or decrease?
The slope INCREASES!
According to the graph the slope gets steeper or increases, but in a negative direction.
What this means is that the velocity slows down with a greater change each second. The deceleration, in this case, get larger even though the velocity decreases.
The velocity goes from 60 to 55 ( a change of 5), then from 55 to 45 ( a change of 10), then from 45 to 30 ( a change of 15), then from 30 to 10 ( a change of 20). Do you see how the change gets LARGER as the velocity gets SMALLER?

44. Area – the “other” basic graph model
Another basic model for understanding graphs in physics is AREA.
Let's try to algebraically make our formulas look like the one above. We'll start with our formula for velocity.
Who gets to play the role of the base? 
Who gets to play the role of the height?
What kind of graph is this?
Time
Velocity
Who gets to play the role of the Area?
A Velocity vs. Time graph  ( velocity = y-axis & time = x-axis)
Displacement

45. Example
What is the displacement during the time interval t = 0 to t = 5 seconds?
That happens to be the area!
What is the displacement during the time interval t = 8 to t = 12 seconds?
Once again...we have to find the area.
During this time period we have a triangle AND a square. We must find the area of each section then ADD them together.

46. Area – the “other” basic graph model
Let's use our  new model again, but for our equation for acceleration.
What does this mean? Who gets to play the role of the base?
Who gets to play the role of the height?
What kind of graph is this?
Who gets to play the role of the Area?
Time
Acceleration
An Acceleration vs. Time graph  ( acceleration = y-axis & time = x-axis)
The Velocity

47. Acceleration vs. Time Graph
What is the velocity during the time interval t = 3 and t = 6 seconds?
Find the Area!

48. Graphing Summary There are 3 types of MOTION graphs
Displacement (position) vs. Time
Velocity vs. Time
Acceleration vs. Time
There are 2 basic graph models
Slope (derivative)
Area (integral)

49. Summary There are 2 directions: L to R = Slope R to L = Area
v (m/s)
a (m/s/s)
x (m)
slope = v
slope = a
area = v
area = x
t (s)
t (s)
t (s)
There are 2 directions:
L to R = Slope
R to L = Area
X-t -> slope -> V-t -> slope -> A-t
A-t <- area <- V-t <- area <- X-t

50. Comparing and Sketching graphs
One of the more difficult applications of graphs in physics is when given a certain type of graph and asked to draw a different type of graph
List 2 adjectives to describe the SLOPE or VELOCITY
The slope is CONSTANT
x (m)
slope = v
The slope is POSITIVE
t (s)
v (m/s)
How could you translate what the SLOPE is doing on the graph ABOVE to the Y axis on the graph to the right?
t (s)

51. Example v (m/s) x (m) 1st line 2nd line 3rd line t (s) t (s)
The slope is constant
The slope is “0”
The slope is “-”
3rd line
The slope is “+”
The slope is constant

52. Example – Graph Matching
Which a-t graph is correct for the v-t shown?
What is the SLOPE of the v-t graph doing?
a (m/s/s)
The slope is increasing
v (m/s)
t (s)
a (m/s/s)
t (s)
t (s)
a (m/s/s)
t (s)

53. Summary of Chapter 2
Motion involves a change in position; it may be expressed as the distance (scalar) or displacement (vector).
A scalar has magnitude only; a vector has magnitude and direction.
Average speed (scalar) is distance traveled divided by elapsed time.
Average velocity (vector) is displacement divided by total time.
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54. Summary of Chapter 2
Instantaneous velocity is evaluated at a particular instant.
Acceleration (vector) is the time rate of change of velocity.
Kinematic equations for constant acceleration:
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55. Summary of Chapter 2 An object in free fall has a = –g.
Kinematic equations for an object in free fall:
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