Accelerated Motion

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Accelerated Motion

• Velocity, acceleration and gravity

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How fast do things fall
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Reflexes
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Position-Time Graphs
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2
3
4
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Velocity v. Time
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Definitions

• Velocity
• Change in position with respect to time
• v ?d/?t
• Which can be written as
• (dfinal-dinitial)/(tfinal-tinitial)
• Common notation
• (dfdi)/(tfti)

• Acceleration
• Change in velocity with respect to time
• a ?v/?t
• Which can be written as
• (vfinal-vinitial)/(tfinal-tinitial)
• Common notation
• (vfvi)/(tfti)

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Velocity to Acceleration

• v?d/?t(dfinaldinitial)/(tfinaltinitial)
• a?v/?t(vfinalvinitial)/(tfinaltinitial)

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Average Acceleration

• a ?v/?t(vfinalvinitial)/(tfinaltinitial)
• f final
• i initial
• If tinitial 0
• a (vfinal vinitial)/tfinal
• Or
• vf vi atf

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Positive and Negative Acceleration
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Practice Problem

• A soccer player is running at a constant velocity
  of 50.0km/h (31mph). The player falls and skids
  to a halt in 4.0 seconds.
• What is the average acceleration of the player
  during the skid?
• What is the plot of the velocity vs. time?

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Practice Problem

• A water balloon in the sling of a water balloon
  launcher undergoes a constant acceleration
  25m/s2 for 1.5s.
• What is the velocity of the water balloon right
  after launch?

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Practice Problem

• A car accelerates from rest at 5 m/s2 for 5
  seconds. It moves with a constant velocity for
  some time, and then decelerates at 5 m/s2 to come
  to rest. The entire journey takes 25 seconds.
  Plot the velocity-time graph of the motion.

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Practice Problem
Determine the accelerations for a1, a2, a3, and
a4 for each time interval.
a1 4/5 a2 (4-4)/(10-5) a3 (16-4)/(20-10) a4
(0-16)/(30-20)
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Frictionless Cars
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Frictionless Car Plots
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Good Reading on Plot
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Velocity with Constant Acceleration

• Given
• Solve
• for tf
• Substitute in
• Yeilds

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Velocity with Constant Acceleration

• Solve for vf

2
½
2
1
1
½
2
2
1
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
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Graphs

• Determine which equations provide the area under
  the graph. (let ti 0)

(vf-vi)
(tf-ti)
½
1)
Velocity (m/s)
2
2)
tf
a
½
3)
(vf-vi)
2
1
(tf-ti)
(tf-ti)
2
Time (s)
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Velocity with Constant Acceleration

• Equation to remember
• vf2 vi2 2a(df-di)

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Position with Average Acceleration

• ?d/?t ?v ½ a ?t
• ?d ?v?t ½ a ?t2
• When ti 0
• df - di vitf ½ atf2

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Position with Average Acceleration

• Equation to remember
• Final position initial position (change in
  velocity)time ½ (acceleration)(time squared)
• df di (vf-vi)t ½ at2

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Table 3-3 Page 68

• Equations of Motion for Uniform Acceleration

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Free Fall on the Moon
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Free Fall on the Moon
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Group Project pg 78

• How fast is the Earth spinning?
• 0.5 km/sec   
• How fast is the Earth revolving around the Sun?
• 30 km/sec   
• How fast is the Solar System moving around the
  Milky Way Galaxy?
• 250 km/sec   
• How fast is our Milky Way Galaxy moving in the
  Local Group of galaxies?
• 370 km/sec

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Free Fall

• All Objects fall at the same speed regardless of
  mass (if you can neglect wind resistance).

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Free Fall

• A ball or a bullet?
• .
• .

Position with Average Acceleration
Height with constant gravity
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Falling
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Poor little guy
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Graphs
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Cart Movement
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Practice Problems

• If you throw a ball straight upward, it will rise
  into the air and then fall back down toward the
  ground.
• Imagine that you throw the ball with an initial
  velocity of 10.0 m/s.
• a. How long does it take the ball to reach the
  top of its motion?
• b. How far will the ball rise before it begins to
  fall?
• c. What is its average velocity during this
  period?

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a. How long does it take the ball to reach the
top of its motion?
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b. How far will the ball rise before it begins to
fall?
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c. What is its average velocity during this
period?
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Practice Problem

• A sudden gust of wind increases the velocity of a
  sailboat relative to the water surface from 3.0
  m/s to 5.5 m/s over a period of 60.0 s.
• a. What is the average acceleration of the
  sailboat?
• b. How far does the sailboat travel during the
  period of acceleration?

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a. What is the average acceleration of the
sailboat?
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b. How far does the sailboat travel during the
period of acceleration?
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Practice Problem

• A car starts from rest with an acceleration of
  4.82 m/s2 at the instant when a second car
  moving with a velocity of 44.7 m/s (100mph by the
  way) passes it in a parallel line. How far does
  the first car move before it overtakes the second
  car?
• Setup an equation or graph

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Setup the equation
0
0
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Positiond
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Velocityv?d/?t
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Accelerationa?v/?t
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