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1 D Kinematics

• Please get a set of notes.
• Remember to be in your seat , quiet and facing
  forward when the bell rings.

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Vector vs. Scalar

• Vectors measurements that have both magnitude
  and direction (displacement, velocity,
  acceleration, force etc.)
• Scalar measurements that have only magnitude
  (distance, speed, mass, etc.)
• Vector measurements and scalar will be equal when
  traveling in one direction.

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Displacement

• Displacement is a change in position.
• Displacements can be negative if they are in a
  negative direction down, south, left or west.
• A displacement can be zero even if an object has
  moved, if the object ends up back in the same
  position as it started in.

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Velocity

• Velocity is a change in displacement in a given
  amount of time.
• This formula gives average velocity and cannot be
  used accurately when there is not constant
  velocity.

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Acceleration

• Acceleration is a change in velocity in a given
  period of time.
• This means speeding up, slowing down or changing
  directions!
• Our kinematic formulas for acceleration only work
  when uniform acceleration has occurred.

• Vf Vi at
• d Vit ½ at2
• Vf2 Vi2 2ad

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Direction of Accleration

• If an object is slowing down, then its
  acceleration is in the opposite direction of its
  motion.
• If an object is speeding up, then its
  acceleration is in the same direction of its
  motion.

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Sample Acceleration Problem

• A race car enters the race track from the pits
  traveling at a velocity of 48 m/s north. Its
  velocity increases at a rate of 10 m/s2 for 12
  seconds. What is the new velocity of the race
  car?

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Acceleration Due to Gravity

• Problems involving the acceleration of gravity
  are really just simplified versions of our
  regular acceleration problems.
• When the only force accelerating and object is
  gravity (free-fall) the acceleration is always
  known to be about 9.8 m/s2 (if the problem occurs
  on Earth)

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Simplified Kinematics

• If the initial velocity of the object is zero, we
  can simplify all of our kinematics to the forms
  found at the right.

• Vf at
• d ½ at2
• Vf2 2ad

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Sample Problem

• A baseball is dropped from a blimp that is 213 m
  in the air (about 700 ft). How fast is the ball
  going when it impacts a baseball players mitt?
  (good ole Joe Sprinz). Assume air resistance is
  negligible and Joe catches the ball at ground
  level.
• How long is the ball in the air?

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Graphing Motion

• Another important skill we need to review is
  interpreting motion.
• Most common graphs
• Displacement vs. time
• Velocity vs. time

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Graphing Motion

• Constant positive velocity

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Graphing Motion

• Constant negative velocity why is it negative?

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Graphing Motion

• Positive velocity, positive acceleration

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Graphing Motion

• Positive velocity, negative acceleration

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Graphing Motion

• negative velocity, negative acceleration

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Graphing Motion

• negative velocity, positive acceleration

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Graphing Motion

• Remember the slope of a position-time graph is
  velocity
• Remember the slope of a velocity-time graph is
  acceleration.
• Remember the area of a velocity-time graph is
  displacement.

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Practice Problems

• Use the principle of slope to describe the motion
  of the objects depicted by the two plots below.
  In your description, be sure to include such
  information as the direction of the velocity
  vector (i.e., positive or negative), whether
  there is a constant velocity or an acceleration,
  and whether the object is moving slow, fast, from
  slow to fast or from fast to slow. Be complete in
  your description.

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Determining Slope

• Dont forget the formula to determine slope!!

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Practice Problem

• Consider the graph at the right. The object whose
  motion is represented by this graph is ...
  (include all that are true)
• a. moving in the positive direction. b. moving
  with a constant velocity.
• c. moving with a negative velocity.
• d. slowing down.
• e. changing directions.
• f. speeding up.
• g. moving with a positive acceleration.
• h. moving with a constant acceleration.

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Dont Forget These Formulas!
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Practice Problem

• Now try the following two practice problems as a
  check of your understanding. Determine the
  displacement (i.e., the area) of the object
  during the first 4 seconds (Practice A) and from
  3 to 6 seconds (Practice B).
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Practice Problem

• Now try the following two practice problems as a
  check of your understanding. Determine the
  displacement of the object during the first
  second (Practice A) and during the first 3
  seconds (Practice B).