Chapter 2 - Motion in One Dimension

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Chapter 2 - Motion in One Dimension

• 2.1 - Displacement and Velocity

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Motion

• One-dimensional motion is the simplest form of
  motion
• e.g. a train on a straight track (forward or
  backward)
• In this chapter we will consider only
  one-dimensional motion

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Motion

• The first step in analyzing motion is to choose a
  frame of reference.
• If an object is at rest, its position does not
  change with respect to a frame of reference.
• When we choose this frame of reference, we need
  to remember to remain consistent.

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Displacement

• Displacement is the change in position of an
  object.
• It is the length of the straight line drawn from
  its initial position to its final position

Displacement change in position final
position - initial position
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Displacement

• Displacement is not always equal to the distance
  traveled

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Displacement

• Displacement can be positive or negative

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Average Velocity

• Knowing the distance traveled or the displacement
  doesnt tell completely describe the motion of an
  object
• Knowing the speed is important for evaluating
  motion
• Average velocity is the total displacement
  divided by the time interval during which the
  displacement occurred

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Average Velocity

• The Average Velocity can be positive or negative
• Equal to the constant velocity needed to cover
  the given displacement in a given time interval
• It is NOT the average of the starting and ending
  velocities
• Example A car travels from city A to city B (100
  km). If the first half of the distance is driven
  at 50 km/h and the second half is driven at 100
  km/h, what is the average velocity of the car?

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Practice

• Page 44, Practice 2A

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Average Speed

• Velocity is not the same as speed
• Velocity has both magnitude AND direction
• Speed has only a magnitude

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Graphical Interpretation of Velocity

• In a position-time graph, we can determine the
  vavg by drawing a straight line between two
  points on the graph

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Graphical Interpretation of Velocity
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Instantaneous Velocity

• The velocity of an object at some instant

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Chapter 2

• Section 2.2 - Acceleration

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Acceleration

• Most objects in motion dont move with a constant
  velocity
• Acceleration measures the rate of change in
  velocity in a given time interval

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Problem

• Find the acceleration of an amusement park ride
  that falls from rest to a speed of 28m/s in 3.0s.
• 9.3 m/s2

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Acceleration

• Acceleration has both magnitude and direction
• If an object (i.e. a car) is moving in the
  positive direction and is speeding up, the
  acceleration is positive
• If an object is moving in the positive direction
  and is slowing down, the acceleration is negative
• If an object (i.e. a car) is moving in the
  negative direction and is speeding up, the
  acceleration is negative
• If an object is moving in the negative direction
  and is slowing down, the acceleration is positive

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Constant acceleration

• The slope of a velocity-time graph gives the
  acceleration
• When acceleration is constant, the velocity is
  increased by the same amount during each time
  interval.
• The displacement for each time interval increases
  by the same amount

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Displacement

• Depends on
• Initial velocity
• Acceleration
• Time

When acceleration is constant, Vavg is the
average of Vi and Vf
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Displacement

• When acceleration is constant

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Displacement

• The area under the curve in a graph of velocity
  versus time equals the displacement during the
  time interval

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Problem

• A bicyclist accelerates from 5.0 m/s to a
  velocity of 16 m/s in 8 s. Assuming uniform
  acceleration, what distance does the bicyclist
  travel during this time interval?
• 84m

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Final Velocity

• Depends on
• Initial velocity
• Acceleration
• Time

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Constant Acceleration
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Displacement with constant uniform acceleration
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Final velocity after any displacement
Remember that the square root may be either
positive or negative
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Problem

• An aircraft has a landing speed of 302 km/h. The
  landing area of an aircraft carrier is 195 m
  long. What is the minimum uniform acceleration
  required for a safe landing?
• -18.0 m/s2

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Summary
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HW Assignment

• Page 49, Practice 2B, 1 and 4
• Page 53, Practice 2C, 3 and 4
• Page 55, Practice 2D, 2 - 4
• Page 58, Practice 2E, 2, 5, 6

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Chapter 2

• Section 2.3 - Falling Objects

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Free Fall

• Motion of an object falling with a constant
  acceleration
• In the absence of air resistance all objects
  dropped near the surface of a planet fall with
  the same constant acceleration
• The symbol for free-fall acceleration is g
• At the surface of the earth, the magnitude of g
  is approximately 9.81 m/s2.

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Free Fall

• This acceleration is directed downwards
• a -g -9.81 m/s2
• What goes up, must come down
• Fig 2-15, pg 61
• Initial velocity of 10.5 m/s, acceleration is
  -9.81 m/s2
• After 1 s, v 0.69 m/s, acceleration is
  -9.81m/s2
• After 2 s, v -9.12 m/s (directed downward), a
  9.81 m/s2

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Free Fall
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Free Fall

• FREELY FALLING OBJECTS ALWAYS HAVE THE SAME
  DOWNWARD ACCELERATION

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Problem

• A ball is thrown straight up into the air at an
  initial velocity of 25.0 m/s. Create a table
  showing the balls position, velocity, and
  acceleration each second for the first 5.00 s of
  its motion.
• Find the balls time, position, velocity, and
  acceleration at the top of its flight

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HW Assignment

• Pages 72 - 75 34, 38, 40, 41, 46, 50, 56