Motion Along a Straight Line

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Chapter 2 Motion Along a Straight Line
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• Linear motion
• In this chapter we will consider moving objects
• Along a straight line
• With every portion of an object moving in the
  same direction and at the same rate
  (particle-like motion)

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• Types of physical quantities
• In physics, quantities can be divided into such
  general categories as scalars, vectors, matrices,
  etc.
• Scalars physical quantities that can be
  described by their value (magnitude) only
• Vectors physical quantities that can be
  described by their value and direction

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• Distance, position, and displacement
• Distance (scalar) a total length of the path
  traveled regardless of direction (SI unit m)
• In each instance we choose an origin a
  reference point, convenient for further
  calculations
• Position of an object (vector) is described by
  the shortest distance from the origin and
  direction relative to the origin
• Displacement (vector) a change from position
  xi to position xf

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• Velocity and speed
• Average speed (scalar) - a ratio of distance
  traveled (over a time interval) to that time
  interval (SI unit m/s)
• Average velocity (vector) - a ratio of
  displacement (over a time interval) to that time
  interval
• Instantaneous velocity (vector) velocity at a
  given instant
• Instantaneous speed (scalar) a magnitude of an
  instantaneous velocity

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Velocity and speed
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Velocity and speed
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• Instantaneous velocity
• The instantaneous velocity is the slope of the
  line tangent to the x vs. t curve
• This would be the green line
• The light blue lines show that as ?t gets
  smaller, they approach the green line

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• Acceleration
• Average acceleration (vector) - a ratio of
  change of velocity (over a time interval) to that
  time interval (SI unit (m/s)/s m/s2)
• Instantaneous acceleration (vector) a rate of
  change of velocity at a given instant

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• Acceleration
• The slope (green line) of the velocity-time
  graph is the acceleration
• The blue line is the average acceleration

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Chapter 2 Problem 15
An object moves along the x axis according to the
equation x(t) (3.00 t2 - 2.00 t 3.00) m,
where t is in seconds. Determine (a) the average
speed between t 2.00 s and t 3.00 s, (b) the
instantaneous speed at t 2.00 s and at t 3.00
s, (c) the average acceleration between t 2.00
s and t 3.00 s, and (d) the instantaneous
acceleration at t 2.00 s and t 3.00 s.
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• Case of constant acceleration
• Average and instantaneous accelerations are the
  same
• Conventionally
• Then

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• Case of constant acceleration
• Average and instantaneous accelerations are the
  same
• Conventionally
• Then

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Case of constant acceleration
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Case of constant acceleration
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Case of constant acceleration To help you solve
problems
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Chapter 2 Problem 28
A particle moves along the x axis. Its position
is given by the equation x 2 3t - 4t2, with x
in meters and t in seconds. Determine (a) its
position when it changes direction and (b) its
velocity when it returns to the position it had
at t 0.
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• Case of free-fall acceleration
• At sea level of Earths mid-latitudes all
  objects fall (in vacuum) with constant (downward)
  acceleration of
• a - g - 9.8 m/s2 - 32 ft/s2
• Conventionally, free fall is along a vertical
  (upward) y-axis

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Chapter 2 Problem 38
A ball is thrown directly downward, with an
initial speed of 8.00 m/s, from a height of 30.0
m. After what time interval does the ball strike
the ground?
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Alternative derivation Using definitions and
initial conditions we obtain
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical representation
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Graphical integration
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Graphical integration
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Answers to the even-numbered problems Chapter
2 Problem 4 (a) 50.0 m/s (b) 41.0 m/s
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• Answers to the even-numbered problems
• Chapter 2
• Problem 6
• 27.0 m
• 27.0 m (18.0 m/s)?t (3.00 m/s2)(?t)2
• 18.0 m/s

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Answers to the even-numbered problems Chapter
2 Problem 12 (b) 1.60 m/s2 0.800 m/s2
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• Answers to the even-numbered problems
• Chapter 2
• Problem 20
• 6.61 m/s
• -0.448 m/s2

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Answers to the even-numbered problems Chapter
2 Problem 38 1.79 s
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Answers to the even-numbered problems Chapter
2 Problem 48 (b) 3.00 10-3 s (c) 450 m/s
(d) 0.900 m