Accelerated Motion

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Accelerated Motion
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Changing motion

• You can feel the difference between uniform and
  nonuniform motion
• When motion changes, you feel a push or pull (a
  force).
• Ex a Marta train coming to a sudden stop
• In uniform motion, your body becomes used to it.
• Ex sitting in a car on cruise control

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Acceleration

• Whenever we change our state of motion, we are
  accelerating.
• Acceleration is how quickly we are changing our
  velocity
• Acceleration the rate at which velocity is
  changing
• SI unit m/s2 or meters per second per second
• Ex speeding up, slowing down (negative
  acceleration), changing direction

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Check Your Understanding

• If a dog chases its tail in a circle at the same
  speed the whole time, is it accelerating?
• Yes! Even though its speed is staying constant,
  it is changing direction, and therefore changing
  its velocity. If the velocity changes, it is
  accelerating.

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• Equation a ?v / t (vf vi) / t
• a acceleration (m/s2)
• ?v change in velocity (m/s)
• vf final velocity (m/s)
• vi initial velocity (m/s)
• t time (s)

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Check Your Understanding

• Suppose a car moving in a straight line steadily
  increases its speed each second, first from 35 to
  40 km/h, then from 40 to 45 km/h, then from 45 to
  50 km/h. What is its acceleration?
• We see that the speed increases by 5 km/h each
  second. The acceleration would be 5 km/h.s
  during each interval.

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Check Your Understanding

• In 5 seconds a car moving in a straight line
  increases its speed from 50 km/h to 65 km/h,
  while a truck goes from rest to 15 km/h in a
  straight line. What is the acceleration of each
  vehicle?
• a ?v / t
• acar ? atruck ?
• ?vcar655015 km/h ?vtruck15-015 km/h
• t 5s t 5s
• acar (15 km/h) / (5s) atruck (15 km/h)
  / (5s)
• acar 3 km/h.s atruck 3 km/h.s

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Check Your Understanding

• Which undergoes a greater acceleration?
• Although the speeds are different, their rate of
  change of speed is the sameso both have the same
  acceleration.

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Elapsed Time

• Elapsed time the time that has passed since the
  beginning of a fall
• How long it takes something to fall
• SI unit seconds

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Free Fall

• Consider an apple falling from a tree. We know
  that it starts at rest and gains speed as it
  falls, or accelerates.
• Gravity causes the apple to accelerate downward
  and is said to be in free fall.
• Free fall when an object is only affected by
  gravity
• SI unit m/s2 ( for acceleration due to gravity)
• Ex g 10 m/s2 on Earth.
• The letter g represents the acceleration due to
  gravity.

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• Equation v gt
• v velocity or speed (m/s)
• g acceleration due to gravity (10 m/s2 on
  Earth)
• t elapsed time (s)
• Hint - as soon as you see any of the following
  phrases in a word problem, write g 10 m/s2 for
  a given free fall, falling, dropped, thrown

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Check Your Understanding

• What would the speedometer reading on a falling
  rock be 4.5 seconds after it drops from rest?
• v ?
• g 10 m/s2
• t 4.5s
• v gt
• v (10 m/s2) (4.5s)
• v 45 m/s

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• How about 8 seconds?
• v ?
• g 10 m/s2
• t 8s
• v gt
• v (10 m/s2) (8s)
• v 80 m/s
• How about 15 seconds?
• v ?
• g 10 m/s2
• t 15s
• v gt
• v (10 m/s2) (15s)
• v 150 m/s

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• Now consider an object thrown straight up. It
  will continue to move straight up, then it comes
  back down.
• At the highest point, the object changes its
  direction and the objects instantaneous speed is
  0 m/s.
• Whether the object is moving up or down, the
  acceleration of the object is always 10 m/s2.

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• Because an object in free fall increases the rate
  of distance covered every second, we cannot use v
  d/t.
• Equation d ½ gt2
• d distance (m)
• g acceleration due to gravity (10 m/s2 on
  Earth)
• t elapsed time (s)

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Check Your Understanding

• What is the distance an object falls in one
  second?
• d ?
• g 10 m/s2
• t 1 s
• d ½ gt2
• d ½ (10)(12)
• d 5 m

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Air Resistance and Free Fall

• All objects fall at 10 m/s2 on Earth
• Regardless of weight or mass
• Ex In a vacuum, a feather and a bowling ball
  will hit the ground at the same time if dropped
  from the same hieght
• A vacuum is anything without any air (ex outer
  space)
• Air resistance causes objects such as a coin and
  a feather to accelerate differently.
• However, air resistance less noticeably affects
  the motion of more massive objects like stones
  and baseballs.
• With negligible air resistance, falling objects
  can be considered to be in free fall.

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Velocity Time Graphs

• Velocity-Time graphs show the change of velocity
  over an elapsed time
• AKA Speed-Time graphs
• Remember that speed does NOT take into account
  direction
• Time is always the independent variable
• Velocity is always the dependent variable

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• The slope of a Velocity-Time graph is equal to
  acceleration
• Slope rise/run
• Slope change in velocity / time
• a ?v / t
• The steeper the slope, the faster the
  acceleration
• Remember acceleration can be speeding up, slowing
  down, or sharp turns
• A positive slope is speeding up and moving
  forward
• A negative slope is EITHER slowing down OR moving
  backwards
• A zero slope means that the velocity is NOT
  changing, meaning that the object is moving at
  the same speed in the same direction

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Check Your Understanding

• Which person(s) could be slowing down?
• Person C. They have a negative slope they could
  be moving backwards too (there is not enough info
  on the graph to tell).

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Check Your Understanding

• Which person(s) are not accelerating?
• A and E. Their have a constant velocity.
• Which person(s) could be speeding up?
• B and D. They are increasing velocity each
  second.