Chapter 2: Kinematics

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Chapter 2 Kinematics

• 2.1 Motion in One Dimension
• 2.2 Uniform Motion
• 2.3 Instantaneous Velocity
• 2.4 Finding Position from Velocity
• 2.5 Motion with Constant Acceleration
• 2.6 Free Fall
• 2.7 Motion on an Inclined Plane
• 2.8 Instantaneous Acceleration

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Motion in one dimension

• Determining the signs of position, velocity and
  acceleration

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Position vs time graphs
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Interpreting a position graph
1.What is the position at t 0min 2.What is the
position at t 30min 3.What is the velocity at t
20min 4.What is the velocity at t 40min
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Uniform Motion

• V(avg) comstant
• The position-vs-graph is a straight line
• Vs ?s/ ?t
• Sf Si Vs ?t

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Position vs time

• What we can learn in this Figure?(a) what is the
  velocity
• during A? (b) what is the velocity during B? (c)
  what is
• Velocity during C?

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Instantaneous velocity

• Using motion diagrams and graphs

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Stop to think 2.2
C
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quizzes

• Graph a vs b which is horizontal axis?
• How to find the slop of a straight-line graph?
• y/x or ?y/ ?x?
• Does the slop have units? If yes, how to
  determine the units?
• How to find the slop at a point on a
  curvilinear graph?

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Relating a velocity graph to a position graph
The value of the velocity at Any time equals the
slope of The position graph
T
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• Using calculus to find the velocity
• Ex. A particles position is given by the
  function
• 1.What is particles position at t 2s?
• x -86 -2 m
• 2. What is the velocity at t 2s
• Vt2 -3(2)23-9 m/s

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Finding position from Velocity
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Example 2.10
Where is particles turning point?
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Motion with constant acceleration
Definition of acceleration
If set t00s, ?t t
See page 57
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Example 2.14A rocket sled accelerates at 50m/s2
for 5.0 s. Coasts for 3.0 s, then deploys a
parachute and decelerates at 3.0m/s2 until coming
to a halt.
What is the maximum velocity of the rocket
sled? What is the total distance traveled?
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Free Fall
g 9.8m/s2 If we choose the y-axis to point
vertically up
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Example 2.16 A falling rockA rock is released
from rest at the top of 100-m-tall building.How
long does the rock take to fall to the ground,
what is impact velocity?

• Y0100m Y10m
• Vy0 0 m/s t0 0 s

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Motion on an inclined plane
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Instantaneous Acceleration
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Homework 2.54

• A 1000Kg weather rocket is launched straight up.
  The rocket motor provides a constant acceleration
  for 16s, then the motor stops. The rocket
  altitude 20 s after launch is 5100m. You can
  ignore the air resistance
• a) What was the rockets acceleration during the
  first 16 s.
• The rocket launched with Vo 0, after 16 s
• b) After motor stops, the acceleration is g as
  free fall.
• c) The rockets speed as it passes through a
  cloud 5100m above the ground

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Answer the following questionsTwo stones are
release from rest at certain height on after the
other

• A) Will the difference in their speed increase,
  decrease or stay the same
• Suppose, two stones are release from height h,
  second stone releases
• after ?t time from first stone.
• At any time t, the speed of first stone V1 0
  gt, and V2 0 g(t- ?t )
• So that V1-V2 g ?t , since g is constant,
  (V1-V2) is constant too.
• B) Will their separation distance increase,
  decrease or stay the same