Branches of Physics

1
Branches of Physics
2
Branches of Physics

• Study of how things move without considering the
  cause of motion. This branch of physics only
  deals with describing how something is moving
  using quantities like distance, position,
  displacement, speed, velocity and acceleration.

3
Branches of Physics

• Study of how things move or don't move without
  considering the cause of motion. This branch of
  physics only deals with describing how something
  is moving using quantities like distance,
  position, displacement, speed, velocity and
  acceleration.
• Kinematics

4
Branches of Physics

• Study of why things move or don't move in a
  certain way. This branch of physics deals with a
  quantity called net force, which determines
  whether something accelerates or doesn't
  accelerate. This branch of physics deals with
  the causes of motion.

5
Branches of Physics

• Study of why things move or don't move in a
  certain way. This branch of physics deals with a
  quantity called net force, which determines
  whether something accelerates or doesn't
  accelerate. This branch of physics deals with
  the causes of motion.
• Dynamics

6
Branches of Physics

• Study of why things move or don't move in a
  certain way. This branch of physics deals with a
  quantity called net force, which determines
  whether something accelerates or doesn't
  accelerate. This branch of physics deals with
  the causes of motion.
• Dynamics
• Study of both how and why things move, or
• Kinematics Dynamics ??

7
Branches of Physics

• Study of why things move or don't move in a
  certain way. This branch of physics deals with a
  quantity called net force, which determines
  whether something accelerates or doesn't
  accelerate. This branch of physics deals with
  the causes of motion.
• Dynamics
• Study of both how and why things move, or
• Kinematics Dynamics Mechanics

8
Famous Kinematic Quantities
9
Famous Kinematic Quantities

• Tells us how far something travels along a path

10
Famous Kinematic Quantities

• Tells us how far something travels along a path
• distance or change-in distance

11
Famous Kinematic Quantities

• Tells us how far something travels along a path
• distance or change-in distance

B
A
12
Famous Kinematic Quantities

• Tells us how far something travels along a path
• distance or change-in distance

B
Does depend on path taken
A
13
Famous Kinematic Quantities

• Tells us how far something travels along a path
• distance or change-in distance

B
Does depend on path taken
A
d or ?d
14
Famous Kinematic Quantities

• Tells us the straight-line distance and direction
  from start to finish.

B
A
d or ?d
15
Famous Kinematic Quantities

• Tells us the straight-line distance and direction
  from start to finish. Displacement

B
A
d or ?d
16
Famous Kinematic Quantities

• Tells us the straight-line distance and direction
  from start to finish. Displacement

B
Does not depend on path taken, only start and
finish
A
d or ?d
17
Famous Kinematic Quantities

• Tells us the straight-line distance and direction
  from start to finish. Displacement

B
Does not depend on path taken, only start and
finish
?d
A
d or ?d
18
Famous Kinematic Quantities

• Tells us the straight-line distance and direction
  from start to finish. Displacement

B
Does not depend on path taken, only start and
finish
?d
Definition of displacement change of position
A
d or ?d
19
More Kinematics Quantities

• Tells us where something is relative to some
  given reference point

20
More Kinematics Quantities

• Tells us where something is relative to some
  given reference point
• Position

21
More Kinematics Quantities

• Tells us where something is relative to some
  given reference point
• Position
• Definition straight line distance and direction
  of something relative to a reference point

22
More Kinematics Quantities

• Tells us where something is relative to some
  given reference point
• Position
• Definition straight line distance and direction
  of something relative to a reference point
• Symbol ???

23
More Kinematics Quantities

• Tells us where something is relative to some
  given reference point
• Position
• Definition straight line distance and direction
  of something relative to a reference point
• Symbol

d
24
Position Example

• State the position of the stick man relative to
  the school.

32º
N
School
53 m
E
d
??
25
Position Example

• State the position of the stick man relative to
  the school.

32º
N
School
53 m
E
d
53 m E32S or S58E
26
Comparison of Position and Displacement

• Position

• Displacement

27
Comparison of Position and Displacement

• Position
• vector

• Displacement
• vector

28
Comparison of Position and Displacement

• Position
• vector
• Straight line distance and direction of something
  from a given reference point

• Displacement
• vector

29
Comparison of Position and Displacement

• Position
• vector
• Straight line distance and direction of something
  from a given reference point

• Displacement
• vector
• Straight line distance and direction from a
  starting position to a finishing position

30
Comparison of Position and Displacement

• Position
• vector
• Straight line distance and direction of something
  from a given reference point
• Involves where something is at one instant in time

• Displacement
• vector
• Straight line distance and direction from a
  starting position to a finishing position

31
Comparison of Position and Displacement

• Position
• vector
• Straight line distance and direction of something
  from a given reference point
• Involves where something is at one instant in time

• Displacement
• vector
• Straight line distance and direction from a
  starting position to a finishing position
• Involves a definite interval of time with a
  starting time and a separate finishing time

32
Speed

• Definition ????

33
Speed

• Definition rate of change of distance or
  change-in distance over change-in time

34
Speed

• Definition rate of change of distance or
  change-in distance over change-in time
• Defining Equation ?????

35
Speed

• Definition rate of change of distance or
  change-in distance over change-in time
• Defining Equation

V ?d/?t
Symbol for speed
36
Speed

• Definition rate of change of distance or
  change-in distance over change-in time
• Defining Equation
• Units ?????

V ?d/?t
Symbol for speed
37
Speed

• Definition rate of change of distance or
  change-in distance over change-in time
• Defining Equation
• Units m/s km/h miles/h cm/s

V ?d/?t
Symbol for speed
38
Two kinds of Speed Average and Instantaneous

• Average Speed

• Instantaneous Speed

39
Two kinds of Speed Average and Instantaneous

• Average Speed
• Use formula v?d/?t

• Instantaneous Speed
• Use formula v?d/?t

40
Two kinds of Speed Average and Instantaneous

• Average Speed
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0

• Instantaneous Speed
• Use formula v?d/?t

41
Two kinds of Speed Average and Instantaneous

• Instantaneous Speed
• Use formula v?d/?t
• ?t t2-t1 is so small that the initial time t1
  is infinitesimally close to t2, therefore vins
  occurs at one instant t1 t2 t

• Average Speed
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0

42
Two kinds of Speed Average and Instantaneous

• Instantaneous Speed
• Use formula v?d/?t
• ?t t2-t1 is so small that the initial time t1
  is infinitesimally close to t2, therefore vins
  occurs at one instant t1 t2 t

• Average Speed
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0
• Slope of secant line of d vs t graph

43
Two kinds of Speed Average and Instantaneous

• Instantaneous Speed
• Use formula v?d/?t
• ?t t2-t1 is so small that the initial time t1
  is infinitesimally close to t2, therefore vins
  occurs at one instant t1 t2 t
• Slope of tangent line of d vs t graph

• Average Speed
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0
• Slope of secant line of d vs t graph

44
Velocity

• Definition ????

45
Velocity

• Definition rate of change of position or
  change-in position over change-in time

46
Velocity

• Definition rate of change of position or
  change-in position over change-in time
• Defining Equation ????
• 
  

47
Velocity

• Definition rate of change of position or
  change-in position over change-in time
• Defining Equation
• 
  V ?d/?t
• 
  

velocity
Change-in position or displacement
48
Velocity

• Definition rate of change of position or
  change-in position over change-in time
• Defining Equation
• 
  V ?d/?t
• Units ?????
• 
  

velocity
Change-in position or displacement
49
Velocity

• Definition rate of change of position or
  change-in position over change-in time
• Defining Equation
• 
  V ?d/?t
• Units m/s km/h m/s cm/min
• 
  

velocity
Change-in position or displacement
50
Two kinds of Velocity Average and Instantaneous

• Instantaneous Velocity

• Average Velocity

51
Two kinds of Velocity Average and Instantaneous

• Instantaneous Velocity
• Use formula v?d/?t

• Average Velocity
• Use formula v?d/?t

52
Two kinds of Velocity Average and Instantaneous

• Instantaneous Velocity
• Use formula v?d/?t

• Average Velocity
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0

53
Two kinds of Velocity Average and Instantaneous

• Instantaneous Velocity
• Use formula v?d/?t
• ?t t2-t1 is so small that the initial time t1
  is infinitesimally close to t2, therefore vins
  occurs at one instant t1 t2 t

• Average Velocity
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0

54
Two kinds of Velocity Average and Instantaneous

• Average Velocity
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0
• Slope of secant line of d vs t graph

• Instantaneous Velocity
• Use formula v?d/?t
• ?t t2-t1 is so small that the initial time t1
  is infinitesimally close to t2, therefore vins
  occurs at one instant t1 t2 t

55
Two kinds of Velocity Average and Instantaneous

• Instantaneous Velocity
• Use formula v?d/?t
• ?t t2-t1 is so small that the initial time t1
  is infinitesimally close to t2, therefore vins
  occurs at one instant t1 t2 t
• Slope of tangent line of d vs t graph

• Average Velocity
• Use formula v?d/?t
• Always involves a definite time interval with a
  distinct initial time t1 and distinct final time
  t2 so ?t t2-t1 ? 0
• Slope of secant line of d vs t graph

56
Acceleration

• Definition ??????

57
Acceleration

• Definition rate of change of velocity or
  change-in velocity over change-in time

58
Acceleration

• Definition rate of change of velocity or
  change-in velocity over change-in time
• Defining Equation ???????

59
Acceleration

• Definition rate of change of velocity or
  change-in velocity over change-in time
• Defining Equation
• a ?v/?t
• ????

Change-in velocity
acceleration
60
Acceleration

• Definition rate of change of velocity or
  change-in velocity over change-in time
• Defining Equation
• a ?v/?t
• (v2 v1)/?t

Change-in velocity
Initial velocity
acceleration
Final velocity
61
Acceleration

• Definition rate of change of velocity or
  change-in velocity over change-in time
• Defining Equation
• a ?v/?t
• (v2 v1)/?t
• equations can be used for constant, average and
  instantaneous accelerations

Change-in velocity
Initial velocity
acceleration
Final velocity
62
Acceleration

• Definition rate of change of velocity or
  change-in velocity over change-in time
• Defining Equation
• a ?v/?t
• (v2 v1)/?t
• equations can be used for constant, average and
  instantaneous accelerations
• Units m/s/s or m/s2 or (km/h)/s
  and more

Change-in velocity
Initial velocity
acceleration
Final velocity
63
Three forms or Ways to get Acceleration

• To get an acceleration, we need a change-in
  velocity. In what ways can the velocity vector
  change?

64
Three forms or Ways to get Acceleration

• To get an acceleration, we need a change-in
  velocity. In what ways can the velocity vector
  change?
• 1. Speeding up...velocity vector increases in
  length when acceleration vector is oriented in
  same direction as initial
  velocity

a
v1
65
Three forms or Ways to get Acceleration

• To get an acceleration, we need a change-in
  velocity. In what ways can the velocity vector
  change?
• 1. Speeding up...velocity vector increases
  in length when acceleration
  vector is oriented in same direction as
  initial velocity
• 2. Deceleration...Velocity vector decreases in
  length when acceleration vector is opposite
  direction as v1 (slowing down)

a
v1
v1
a
66
Three forms or Ways to get Acceleration

• To get an acceleration, we need a change-in
  velocity. In what ways can the velocity vector
  change?
• 3. Changing direction...velocity vector changes
  direction but not magnitude or length when the
  acceleration vector is 90 to the initial
  velocity

v1
a
67
Three forms or Ways to get Acceleration

• To get an acceleration, we need a change-in
  velocity. In what ways can the velocity vector
  change?
• 3. Changing direction...velocity vector changes
  direction but not magnitude or length when the
  acceleration vector is 90 to the initial
  velocity

v1
a
68
Constant Acceleration
69
Constant Acceleration

• If the velocity changes by the same amount during
  equal time intervals

70
Constant Acceleration

• If the velocity changes by the same amount during
  equal time intervals
• Example acceleration of projectiles near the
  earth's surface where air friction is negligible

71
Constant Acceleration

• If the velocity changes by the same amount during
  equal time intervals
• Example acceleration of projectiles near the
  earth's surface where air friction is negligible
• ag g 9.80 m/s2 down or 10.0 m/s2 down

72
Constant Acceleration

• If the velocity changes by the same amount during
  equal time intervals
• Example acceleration of projectiles near the
  earth's surface where air friction is negligible
• ag g 9.80 m/s2 down or 10.0 m/s2 down
• Meaning ????????

73
Constant Acceleration

• If the velocity changes by the same amount during
  equal time intervals
• Example acceleration of projectiles near the
  earth's surface where air friction is negligible
• ag g 9.80 m/s2 down or 10.0 m/s2 down
• Meaning Every second, the velocity changes by
  10.0 m/s down

74
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• ?

75
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up

76
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• ?

77
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up

78
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00
• 3.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up
• ?

79
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00
• 3.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up
• 0.00

80
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00
• 3.00
• 4.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up
• 0.00
• ?

81
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00
• 3.00
• 4.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up
• 0.00
• 10.0 down

82
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00
• 3.00
• 4.00
• 5.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up
• 0.00
• 10.0 down
• ?

83
Constant Acceleration Example projectile fired
upward at 30.0 m/s

• Time (seconds)
• 0.00
• 1.00
• 2.00
• 3.00
• 4.00
• 5.00

• Instantaneous Velocity
• (meters/second)
• 30.0 up
• 20.0 up
• 10.0 up
• 0.00
• 10.0 down
• 20.0 down

84
Deriving the Big Five Constant Acceleration
Formulas
85
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a ????

86
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1)
• ?t

87
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1) We will call this BIG
  FIVE 1a
• ?t

88
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1) We will call this BIG
  FIVE 1a
• ?t
• Multiply both sides of 1a by ?t

89
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1) We will call this BIG
  FIVE 1a
• ?t
• Multiply both sides of 1a by ?t
• ?t a (v2 - v1)

90
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1) We will call this BIG
  FIVE 1a
• ?t
• Multiply both sides of 1a by ?t
• ?t a (v2 - v1)
• Divide both sides by a

91
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1) We will call this BIG
  FIVE 1a
• ?t
• Multiply both sides of 1a by ?t
• ?t a (v2 - v1)
• Divide both sides by a
• ?t (v2 - v1)
• a

92
Deriving the Big Five Constant Acceleration
Formulas

• Acceleration in terms of v1 , v2 and ?t
• a (v2 - v1) We will call this BIG
  FIVE 1a
• ?t
• Multiply both sides of 1a by ?t
• ?t a (v2 - v1)
• Divide both sides by a
• ?t (v2 - v1) We will call this BIG
  FIVE 1b
• a

93
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t

94
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t
• From the previous slide we have
• ?t a (v2 - v1)

95
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t
• From the previous slide we have
• ?t a (v2 - v1)
• Reverse left and right sides (mathematically
  legal)

96
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t
• From the previous slide we have
• ?t a (v2 - v1)
• Reverse left and right sides (mathematically
  legal)
• v2 - v1 ?t a

97
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t
• From the previous slide we have
• ?t a (v2 - v1)
• Reverse left and right sides (mathematically
  legal)
• v2 - v1 ?t a
• Solve for v2

98
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t
• From the previous slide we have
• ?t a (v2 - v1)
• Reverse left and right sides (mathematically
  legal)
• v2 - v1 ?t a
• Solve for v2
• v2 v1 ?t a

99
Deriving the Big Five Constant Acceleration
Formulas

• One more formula with acceleration in terms
  of v1 , v2 and ?t
• From the previous slide we have
• ?t a (v2 - v1)
• Reverse left and right sides (mathematically
  legal)
• v2 - v1 ?t a
• Solve for v2
• v2 v1 ?t a We will call this
  BIG FIVE 1c

100
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t

101
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?

102
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t

103
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t
• Why can't this formula be used for acceleration ?
  0 ?

104
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t
• Why can't this formula be used for acceleration ?
  0 ?
• The above formula can be modified for a ? 0.
  How?

105
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t
• Why can't this formula be used for acceleration ?
  0 ?
• The above formula can be modified for a ? 0.
  How?
• ?d vavg ?t

106
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t
• Why can't this formula be used for acceleration ?
  0 ?
• The above formula can be modified for a ? 0.
  How?
• ?d vavg ?t What is vavg in terms of
  v1 and v2 ?

107
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t
• Why can't this formula be used for acceleration ?
  0 ?
• The above formula can be modified for a ? 0.
  How?
• ?d vavg ?t What is vavg in terms of
  v1 and v2 ?
• ?d (v1 v2) ?t
• 2

108
Deriving the Big Five Constant Acceleration
Formulas

• (2) Displacement ?d in terms of v1 , v2 , and
  ?t
• If an object moves at a constant velocity v for
  ?t, what formula gives us ?d ?
• ?d v ?t
• Why can't this formula be used for acceleration ?
  0 ?
• The above formula can be modified for a ? 0.
  How?
• ?d vavg ?t What is vavg in terms of
  v1 and v2 ?
• ?d (v1 v2) ?t We will call this
  BIG FIVE 2
• 2

109
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a

110
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2

111
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2

112
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2
• Without simplifying, substitute 1c into 2

113
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2
• Without simplifying, substitute 1c into 2
• ?d (v1 v1 ?t a ) ?t
• 2

114
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2
• Without simplifying, substitute 1c into 2
• ?d (v1 v1 ?t a ) ?t
  ??????
• 2

115
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2
• Without simplifying, substitute 1c into 2
• ?d (v1 v1 ?t a ) ?t ?d
  (2v1 ?t a ) ?t
• 2
  2

116
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2
• Without simplifying, substitute 1c into 2
• ?d (v1 v1 ?t a ) ?t ?d
  (2v1 ?t a ) ?t
• 2
  2
• Expand and simplify

117
Deriving the Big Five Constant Acceleration
Formulas

• (3) Displacement ?d in terms of v1 , ?t and a
• Here are BIG FIVE equations 1c and 2
• v2 v1 ?t a 1c ?d (v1
  v2) ?t 2
• 2
• Without simplifying, substitute 1c into 2
• ?d (v1 v1 ?t a ) ?t ?d
  (2v1 ?t a ) ?t
• 2
  2
• Expand and simplify ?d v1 ?t a
  ?t2/2
• 
  

We will call this BIG FIVE equation 3
118
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a

119
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2

120
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2
• Substitute 1b into 2 ???????

121
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2
• Substitute 1b into 2 ?d (v1
  v2)(v2 - v1)
• 2 a

122
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2
• Substitute 1b into 2 ?d (v1
  v2)(v2 - v1)
• ?d (v2 v1)(v2 - v1) 2
  a
• 2 a

123
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2
• Substitute 1b into 2 ?d (v1
  v2)(v2 - v1)
• ?d (v2 v1)(v2 - v1) 2
  a
• 2 a

124
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2
• Substitute 1b into 2 ?d (v1
  v2)(v2 - v1)
• ?d (v2 v1)(v2 - v1)
  2 a
• 2 a ?d
  (v22 v12)
• 2 a

125
Deriving the Big Five Constant Acceleration
Formulas

• (4) Displacement ?d in terms of v1 , v2 and a
• Here are BIG FIVE equations 1b and 2
• ?t (v2 - v1) 1b ?d (v1
  v2) ?t 2
• a 2
• Substitute 1b into 2 ?d (v1
  v2)(v2 - v1)
• ?d (v2 v1)(v2 - v1)
  2 a
• 2 a ?d
  (v22 v12)
• 2 a
  

We will call this BIG FIVE Equation 4
126
Big Five equation 5

• Homework Exercise
• Derive the fifth Big Five equation using one form
  equation 1 and equation 2. This equation is
• ? d v2 ?t - a ?t2/2

127
List of BIG FIVE equationsMemorize these please!!

• (1a) a (v2 - v1) (1b) ?t (v2
  - v1)
• ?t a
• (1c) v2 v1 ?t a (2) ?d (v1
  v2) ?t
• (3) ?d v1 ?t a ?t2/2 2
• (4) ?d (v22 v12) or (4b) v22
  v12 2a?d
• 2a
• (5) ? d v2 ?t - a ?t2/2

128
When can we use the BIG FIVE?

• Only for constant non-zero acceleration

129
When can we use the BIG FIVE?

• Only for constant non-zero acceleration
• Note Vector quantities cannot be multiplied
  together. Some of the BIG FIVE equations appear
  to break this rule. However, if the motion
  analyzed is along a line in one dimension, we can
  get away with multiplying vectors by representing
  them as or integers.

130
When can we use the BIG FIVE?

• Only for constant non-zero acceleration
• Note Vector quantities cannot be multiplied
  together. Some of the BIG FIVE equations appear
  to break this rule. However, if the motion
  analyzed is along a line in one dimension, we can
  get away with multiplying vectors by representing
  them as or integers.
• Example 2a?d 2(10.0 m/s2down)(2.5 m up)
• ?????

131
When can we use the BIG FIVE?

• Only for constant non-zero acceleration
• Note Vector quantities cannot be multiplied
  together. Some of the BIG FIVE equations appear
  to break this rule. However, if the motion
  analyzed is along a line in one dimension, we can
  get away with multiplying vectors by representing
  them as or integers.
• Example 2a?d 2(10.0 m/s2down)(2.5 m up)
• 2(-10)(2.5)

132
When can we use the BIG FIVE?

• Only for constant non-zero acceleration
• Note Vector quantities cannot be multiplied
  together. Some of the BIG FIVE equations appear
  to break this rule. However, if the motion
  analyzed is along a line in one dimension, we can
  get away with multiplying vectors by representing
  them as or integers.
• Example 2a?d 2(10.0 m/s2down)(2.5 m up)
• 2(-10)(2.5)
• -50 ?????

133
When can we use the BIG FIVE?

• Only for constant non-zero acceleration
• Note Vector quantities cannot be multiplied
  together. Some of the BIG FIVE equations appear
  to break this rule. However, if the motion
  analyzed is along a line in one dimension, we can
  get away with multiplying vectors by representing
  them as or integers.
• Example 2a?d 2(10.0 m/s2down)(2.5 m up)
• 2(-10)(2.5)
• -50 50 m2/s2 down

134
What equations do we use for a 0 ?
135
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?

136
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity

137
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?

138
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?
• ?d v ?t

139
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?
• ?d v ?t This is called the LITTLE ONE!!

140
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?
• ?d v ?t
• Note there are two other forms of this same
  equation. What are they?

141
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?
• ?d v ?t
• Note there are two other forms of this same
  equation. What are they?
• ?t ?d/v and v ?d/?t

142
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?
• ?d v ?t
• Note there are two other forms of this same
  equation. What are they?
• ?t ?d/v and v ?d/?t ?d
• v ?t

143
What equations do we use for a 0 ?

• If the acceleration is zero, how do we describe
  the motion?
• a 0 means constant velocity
• There is only one equation that describes motion
  at a constant velocity. What is it ?
• ?d v ?t
• Note there are two other forms of this same
  equation. What are they?
• ?t ?d/v and v ?d/?t ?d
• Again we call this the LITTLE one! v
  ?t