Kinematics

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Kinematics

• (Stuff moving)

(stuff)
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Start with vocabulary

• Position (x) where it is (meters)
• Displacement (Dx) how far it moved, direction
  (/-) is important (meters)
• Velocity (v) how fast it moves, direction is
  important (/-) (meters/second)
• Instantaneous, right now! Slope of tangent
• Average velocity change in position divided by
  change in time

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Vocabulary, continued

• Acceleration (a) rate of change in velocity
• m/s2
• Instantaneous, Slope of velocity time curve
• Average, over time interval
• Our equations apply only to constant acceleration
• When acceleration changes, we break the problem
  into chunks of constant acceleration

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The Equations!
Dont forget these definitions!
All you get on AP Equations Sheet
5
Daddy
6
Mommy
Notice no time in this one!
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The area of a velocity curve is displacement!
v
Avg velocity
area
t
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Tips for deciphering word problems

• at rest, from rest not moving at beginning
  v0 zero!
• ..comes to rest vfzero
• Travels 10 m in 10 sec
• Dx10m, Dt10 s
• reaches a maximum height
• velocity at hmax zero!

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The Equations!
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Kinematics Examples

• Drag race
• Avg velocity given time and disp
• Avg acceleration given final v and disp
• Motion Graphing
• Aircraft Catapult
• Draw position and acceleration given velocity

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Drag Race
1. A car travels 402 .34 meters in 11.963 sec.
What is its average velocity?
2. The same car reached 40.73 m/s at the end of
the first 201.17 meters. What was its average
acceleration?
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Drag Race 1
Given Dx 402 .34 meters in Dt11.963 sec.
Unknown vavg??
Principle Kinematics(where to look for eqn)
Picture
Equation
Simplify/Solve/Substitute
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Drag Race 2
Given vf 40.73 m/s in Dx201.17m
Unknown aavg??
Principle Kinematics(where to look for eqn)
Picture
zero
Equation
Simplify/Solve/Substitute
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Aircraft catapult

• Navy aircraft are launched from the decks of
  aircraft carriers with a steam powered catapult.
  The graph shows the velocity of the aircraft as a
  function of time. Analyze the graph and draw
  corresponding position and acceleration graphs.

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Aircraft Catapult(v)
v(m/s)
50
time(s)
5
16
Aircraft Catapult(a)
a(m/s2)
20
time(s)
5
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Aircraft Catapult(x)
x(m)
300
200
100
time(s)
5
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Freefall

• Same kinematics equations
• Just constant acceleration of
• ag9.8 m/s2
• toward earth. Do yourself a favor and call down
  negative.

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Freefall Example

• 1) A ball is dropped from 10 meters high.
• A)How fast is it going when it hits the ground?
• B) How long does it take to reach the ground?

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Freefall Example

• 2) A ball is given an upward velocity of 5.0 m/s,
  what is the maximum height it will reach?
• 3) How long does it take to reach this max height?

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Freefall Example

• 5) A ball is thrown upward with a velocity of 4.0
  m/s. How fast is it going when it hits the
  ground, 10 meters below where it was thrown from?

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Freefall Cases

• Downy
• Dropping or spiking
• Uppy
• Toss up
• Uppy downy
• Toss up off a ledge, object lands lower than the
  ledge

Establish your coordinate system and be
consistent with signs.
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Wrap up

• Givens
• Unknowns
• PP
• E
• Time or none given
• S S S

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More examples

• More example problems
• Try v0-3.0, a5, Dt4, Dx?
• Try a spike (as in football players touchdown
  celebration)
• xf-5.0, x02.0, v0-1.0, a-9.8, Dt?

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The Equations!
Dont forget definitions
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Drag Race 1
Given Dx 402 .34 meters in Dt11.963 sec.
Unknown vavg??
Principle Kinematics(where to look for eqn)
Picture
Equation
Simplify/Solve/Substitute
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Drag Race 2
Given vf 40.73 m/s in Dx201.17m
Unknown aavg??
Principle Kinematics(where to look for eqn)
Picture
Equation
Simplify/Solve/Substitute
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Aircraft Catapult(v)
v(m/s)
50
time(s)
5
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Aircraft Catapult(a)
a(m/s2)
20
time(s)
5
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Aircraft Catapult(x)
x(m)
300
200
100
time(s)
5
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Freefall Example

• 1) A ball is dropped from 10 meters high.
• A)How fast is it going when it hits the ground?
• B) How long does it take to reach the ground?

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Freefall Example

• 3) A ball is given an upward velocity of 5.0 m/s,
  what is the maximum height it will reach?
• 4) How long does it take to reach this max height?

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Freefall Example

• 5) A ball is thrown upward with a velocity of 4.0
  m/s. How fast is it going when it hits the
  ground, 10 meters below where it was thrown from?