Chapter 3 Motion (CP)

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Chapter 3 Motion (CP)
2
Motion Equations
Under Constant Acceleration
Basic Velocity Equation
Average Velocity Under Constant Acceleration
3
Think About?

1. What is speed?
2. What is velocity?
3. What is acceleration?

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• Section 1 How do the concepts of speed and
  distance, and velocity and displacement relate to
  each other?

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Equations relate things to each other
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Equations can be simplified into symbols
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• Mechanics is the branch of physics that describes
  motion.
• Kinematics describes how objects move.
• This unit will focus on how objects move in
  straight lines (forward and backward).

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Scalar vs. Vector

• Scalars represent magnitudes only (number and
  unit).
• How many slices of pizza did you eat?
• How many steps are in front of the building?
• The answer to these questions is a scalar
  quantity.

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Scalar vs. Vector

• Vectors represent a magnitude and a direction. I
  walked 14 paces North.
• The magnitude in this case is __________________.
  
• The direction is ___________________.

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Scalar vs. Vector

• Vectors represent a magnitude and a direction. I
  walked 14 paces North.
• The magnitude in this case is __________________.
  
• The direction is ___________________.

14 paces
North
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Vocabulary

• Distance (scalar) a measurement of space
  between two objects. (ex. 5m)
• Displacement (vector) how far from where we
  started. (ex. 5m, east)
• Speed (scalar) how fast something is moving.
  (ex. 25 m/s)
• Velocity (vector) how fast we are moving in a
  direction. (ex. 25 m/s. south)

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Problem Set 1

• Are the following scalars or vectors?
• 4 meters east
• The object was 4 meters
• I had 6 donuts
• I ran 6 miles west of the river

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Problem Set 1

• Are the following scalars or vectors?
• 4 meters east (vector)
• The object was 4 meters (scalar)
• I had 6 donuts (scalar)
• I ran 6 miles west of the river (vector)

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Calculating with scalars

• If you are asked for speed or distance
• The equation is similar to the velocity equation

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Lets look at a problem with a scalar quantity

• Ex.1a Joan walks four blocks, turns around, and
  walks two blocks. She walks for 90 seconds.
• How far did Joan walk?
• (since direction does not matter, all movement
  adds up)

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Lets look at a problem with a scalar quantity

• Ex.1a Joan walks four blocks, turns around, and
  walks two blocks. She walks for 90 seconds.
• How far did Joan walk?

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Lets look at a problem with a scalar quantity

• Ex.1b Joan walks four blocks, turns around, and
  walks two blocks. She walks for 90 seconds.
• How fast did Joan walk?
• (take total distance and divide it by time)

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Lets look at a problem with a scalar quantity

• Ex.1b Joan walks four blocks, turns around, and
  walks two blocks. She walks for 90 seconds.
• How fast did Joan walk?

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Adding Vectors

• Before we get into any more detailed math you
  need to learn a bit more about adding vectors and
  the procedure for solving a physics problem

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Adding Vectors

• You must turn the direction into a sign in front
  of the number
• Later, when you have your final answer you will
  take the sign and make it a direction again
• Use this as a general guide ?
• The x axis can only be added or subtracted from
  other x axis vectors
• The y axis can only be added or subtracted from
  other y axis vectors

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Adding Vectors

• Direction matters when adding vectors
• A man goes east 2 km and then west 1 km, what was
  his displacement (from origin)?

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Adding Vectors (simple example)

• A man goes east 2 km and then west 1 km, where
  did he end off?
• 2 km east becomes a d1 of 2 km
• 1 km west becomes a d2 of -1 km
• Now add the two vectors (d1 d2)

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Adding Vectors (simple example)

• A man goes east 2 km and then west 1 km, where
  did he end off?
• 2 km east becomes a d1 of 2 km
• 1 km west becomes a d2 of -1 km
• Now add the two vectors (d1 d2)

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Adding Vectors (simple example)

• A man goes east 2 km and then west 1 km, where
  did he end off?
• 2 km east becomes a d1 of 2 km
• 1 km west becomes a d2 of -1 km
• Then convert it back into a direction

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Problem set 2

1. A dog walks 50 m East and then 23 m West. What
   is its displacement?
2. A bird has flown 850 km South for the winter when
   he realizes he as to go back because it is still
   summer. After traveling 320 km North, what is
   the birds displacement?
3. Mr. Holden starts pacing the room. He goes 3
   meters North, 4 meters South, 5 meters North,
   then 1 meter South. What is his displacement?

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Problem set 2

1. A dog walks 50 m East and then 23 m West. What
   is its displacement?

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Problem set 2

• 2. A bird has flown 850 km South for the winter
  when he realizes he as to go back because it is
  still summer. After traveling 320 km North, what
  is the birds displacement?

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Problem set 2

• 3. Mr. Holden starts pacing the room. He goes 3
  meters North, 4 meters South, 5 meters North,
  then 1 meter South. What is his displacement?

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Review Questions?

• A person walks 5m east for 2s and another walks
  10 m west for 1s.
• 1. What is the Distance traveled?
• 2. What is the displacement after 3 seconds?

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Lets look at the average velocity equation closer
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• v is velocity .. (mks unit m/s)
• d is displacement ... (mks unit m)
• t is time .................. (mks unit s)
• df is final displacement
• do is initial displacement
• tf is final time
• to is initial time

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This equation can be used many different ways
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Follow this process every time!!!

• When solving a problem
• 1. List the given information in a table
• 2. Identify the unknown.
• 3. Use the equation that contains the unknown,
  the given information, and no other variables.
• 4. Substitute.
• 5. Solve.
• 6. Include units on final answers.

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Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans displacement from start to finish?

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Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans displacement from start to finish?

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Lets look at a problem with a vector quantity

• What is Joans displacement from start to finish?

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Lets look at a problem with a vector quantity

• What is Joans displacement from start to finish?

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Lets look at a problem with a vector quantity

• What is Joans displacement from start to finish?

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Lets look at a problem with a vector quantity

• What is Joans displacement from start to finish?

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Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity?

41
Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity?

42
Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity?

43
Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity?

44
Lets look at a problem with a vector quantity

• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity?

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• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity if she walks an
  additional two blocks West?

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• Ex. Joan walks four blocks East, then turns
  around and walks two blocks West. Joan walks for
  three minutes.
• What is Joans average velocity if she walks an
  additional two blocks West?

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Review question

• Which quantities give more information, scalars
  or vectors?

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• Which quantities give more information, scalars
  or vectors?
• Scalars magnitude
• Vectors magnitude and direction

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• Ex. If a car travels 500 m North and 250 m South
  in 1 minute, what is its
• Distance traveled?
• Displacement from where it began?
• Speed?
• Velocity?

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• Ex. If a car travels 500 m North and 250 m South
  in 1 minute, what is its
• Distance traveled?
• Displacement from where it began?

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• Ex. If a car travels 500 m North and 250 m South
  in 1 minute, what is its
• Speed?

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• Ex. If a car travels 500 m North and 250 m South
  in 1 minute, what is its
• Speed?

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• Ex. If a car travels 500 m North and 250 m South
  in 1 minute, what is its
• Velocity?

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• Ex. If a car travels 500 m North and 250 m South
  in 1 minute, what is its
• Velocity?

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• Ex. 2 If one car travels 100 m East for 5 seconds
  and another car travels 80m West for 4 seconds.
  What is the velocity of the cars?

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• Ex. 2 If one car travels 100 m East for 5 seconds
  and another car travels 80m West for 4 seconds.
  What is the velocity of each car?

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• Average velocity describes the objects velocity
  over a period of time.
• Instantaneous velocity describes the objects
  velocity at one instant in time.

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• What would a cars speedometer read?

Average velocity or Instantaneous velocity
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• What would a cars speedometer read?

Average velocity or Instantaneous velocity
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• With all that you now know, can you define
  constant velocity?

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• With all that you now know, can you define
  constant velocity?
• Moving at a constant speed in a certain direction
  without acceleration.
• Constant velocity means a 0 m/s2

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Review Questions?

1. What is a scalar?
2. What is a vector?
3. What are two examples of scalars?
4. What are two examples of vectors?

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Classwork/Homework
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ACCELERATION Chapter 3
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Review Questions?

• A person walks 5m east for 2s and another walks
  10 m west for 1s.
• What is the
• a. distance traveled
• b. displacement
• c. speed
• d. velocity

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• Section 2 How do you apply the concept of
  acceleration to describing an objects motion?

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• Acceleration describes how an objects velocity
  changes with respect to time.
• What is deceleration?
• Can a car move forward without accelerating?
• Can a car move backward without accelerating?
• Can a car move forward and accelerate?
• Can a car move backward and accelerate?
• Can a car move forward and decelerate?
• Can a car move forward and accelerate?

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• Acceleration describes how an objects velocity
  changes with respect to time.
• What is deceleration? Slowing down in the
  direction of travel
• Can a car move forward without accelerating?
• Can a car move backward without accelerating?
• Can a car move forward and accelerate?
• Can a car move backward and accelerate?
• Can a car move forward and decelerate?
• Can a car move forward and accelerate?

Yes to all- think about each scenario
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• Average acceleration equals the change in
  velocity divided by time.
• Can you write this using symbols?
• What are the appropriate units for acceleration?

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• Unit for acceleration is m/s/s or m/s2

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• Acceleration can either be a positive or negative
  change in motion. If it is negative, then the
  object is decelerating (slowing down).
• If an object has a velocity and acceleration in
  the positive direction, how will the object
  travel?

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• What are 3 things in your car that can cause
  acceleration?

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• What are 3 things in your car that can cause
  acceleration?
• Gas petal
• Break
• Steering Wheel

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Problem Set 4

• What does the following ask for or tell us about
  any of our variables?
• How fast was it going?
• How fast will it go?
• Object Starts at rest?
• Object slows down?
• Object comes to a stop?

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Problem Set 4

• What does the following ask for or tell us about
  any of our variables?
• How fast was it going?
• How fast will it go?
• Object Starts at rest?
• Object slows down?
• Object comes to a stop?

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• Ex1 A car accelerates from a traffic light and
  increases its velocity form 0m/s to 20m/s in 5
  seconds. What is its acceleration?

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• Ex1 A car accelerates from a traffic light and
  increases its velocity form 0m/s to 20m/s in 5
  seconds. What is its acceleration?

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• A car accelerates from a traffic light and
  increases its velocity form 0m/s to 20m/s in 5
  seconds. What is its acceleration?
• Ex The same car then travels for 10 seconds at
  a constant velocity of 20m/s. What is its
  average acceleration over that ten second period?
  

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• A car accelerates from a traffic light and
  increases its velocity form 0m/s to 20m/s in 5
  seconds. What is its acceleration?
• Ex The same car then travels for 10 seconds at
  a constant velocity of 20m/s. What is its
  average acceleration over that ten second period?
  

80

• A car accelerates from a traffic light and
  increases its velocity form 0m/s to 20m/s in 5
  seconds. What is its acceleration?
• Ex The same car then travels for 10 seconds at
  a constant velocity of 20m/s. What is its
  average acceleration over that ten second period?
  What is the average acceleration over the entire
  15 seconds?

81

• A car accelerates from a traffic light and
  increases its velocity form 0m/s to 20m/s in 5
  seconds. What is its acceleration?
• Ex The same car then travels for 10 seconds at
  a constant velocity of 20m/s. What is its
  average acceleration over that ten second period?
  What is the average acceleration over the entire
  15 seconds?

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• Ex Finally, the car decelerates at 0.5m/s2.
  How long will it take for the car to come to a
  complete stop?

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• Ex Finally, the car decelerates at 0.5m/s2.
  How long will it take for the car to come to a
  complete stop?

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Classwork/Homework

• CP
• 1D motion packet pg 2 (problems 4-6)

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Day 4 Intro

• 1. Mike can go from 0 m/s to 15 m/s in 5
  seconds. What is Mikes acceleration?
• 2. Mike decelerates from 15 m/s to rest at 4.5
  m/s2. How long does this take Mike?

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Section 3 How do I apply the equations for
constant acceleration to problem solving?

• Note
• Real-world acceleration/deceleration rates are
  variable. We simplify the problems and
  approximate their rates as uniform/constant.
• The following problems will assume uniform
  acceleration.

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Remember to follow this process every time!!!

• When solving a problem involving uniform
  acceleration
• 1. List the given information in a table
• 2. Identify the unknown.
• 3. Use the equation that contains the unknown,
  the given information, and no other variables.
• 4. Substitute.
• 5. Solve.
• 6. Include units on final answers.

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Note

• There may be more than one way to solve a
  problem. Its important to work with consistent
  units. For example, if the displacement is
  measured in meters and the velocity is measured
  in km/hr, you will need to convert units.

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Uniform acceleration equations
vf vo at
What does each variable stand for? ______________
_ vf vo a ?d t
vf2 vo2 2a?d
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Uniform acceleration equations
vf vo at
What does each variable stand for? ______________
_ vf final velocity vo initial
velocity a acceleration ?d displacement t
time
vf2 vo2 2a?d
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• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?
• Write your givens and needs, then pick your
  equation

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• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?

93

• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?

94

• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?

Only one that is left
95

• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?

96

• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?
• How much time did it take?

97

• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?
• How much time did it take?

98

• Ex. A car accelerates from rest to a final speed
  of 40m/s in 100m. What is the cars
  acceleration?
• How much time did it take?

99

• Ex. 2 A car traveling at 25m/s accelerates at
  5m/s2 for 5 seconds. How far does the car travel?

100

• Ex. 2 A car traveling at 25m/s accelerates at
  5m/s2 for 5 seconds. How far does the car travel?

101

• Ex. 2 A car traveling at 25m/s accelerates at
  5m/s2 for 5 seconds. How far does the car travel?

102

• Ex. 2 A car traveling at 25m/s accelerates at
  5m/s2 for 5 seconds. How far does the car travel?

103

• Ex. 2 A car traveling at 25m/s accelerates at
  5m/s2 for 5 seconds. How far does the car travel?
  
• What is its final velocity?

104

• Ex. 2 A car traveling at 25m/s accelerates at
  5m/s2 for 5 seconds. How far does the car travel?
  
• What is its final velocity?

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Classwork/Homework

• CP 1D Motion Problems (pg2) 7,8,9,10