Motion in One Dimension

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Chapter 2

• Motion in One Dimension

2
Kinematics

• In kinematics, you are interested in the
  description of motion
• Not concerned with the cause of the motion

3
Quantities for Motion

• Motion involves three concepts
• Displacement, Distance
• Velocity, Speed
• Acceleration

4
Position

• Defined in terms of a frame of reference
• One dimensional, so generally the x- or y-axis
• Defines a starting point for the motion

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Displacement

• Defined as the change in position
• May be represented as ?y if vertical

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Distance

• Distance relates to the actual path traveled.
• Displacement only depends on a different from
  start to end.
• Think of displacement as a net quantity.

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Graph of Position with Time
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Vector and Scalar Quantities

• Vector quantities need both magnitude (size) and
  direction to completely describe them
• Generally denoted by boldfaced type or an arrow
  over the letter
• or sign is sufficient
• Scalar quantities are completely described by
  magnitude only

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Speed

• The average speed of an object is defined as the
  total distance traveled divided by the total time
  elapsed
• Speed is a scalar quantity (units m/s)

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Velocity

• It takes time for an object to undergo a
  displacement
• The average velocity is the rate at which the
  displacement occurs
• Direction will be the same as the direction of
  the displacement

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Speed vs. Velocity

• Cars on both paths have the same average velocity
  since they had the same displacement in the same
  time interval
• The car on the blue path will have a greater
  average speed since the distance it traveled is
  larger

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Constant Velocity

• The straight line indicates constant velocity
• The slope of the line is the value of the average
  velocity

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Complex velocity

• The red line is for a time changing velocity
• The average velocity is the slope of the blue
  line joining two points

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Instantaneous Velocity

• The limit of the average velocity as the time
  interval becomes infinitesimally short (I.e., as
  the time interval approaches zero)
• The instantaneous velocity is what happens at
  each point of time
• Its value is a tangent line at a point

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Acceleration

• Changing velocity means an acceleration is
  present
• Acceleration is the rate of change of the
  velocity
• Units are m/s2 (SI), cm/s2 (cgs), and
• ft/s2 (US Cust)

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Average Acceleration
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Acceleration Quiz

1. A car is traveling east and slowing down. Which
   direction is its acceleration?
2. Is the acceleration considered to be positive or
   negative?
3. What is the speed of an object like (stopped,
   increasing, decreasing, or coasting) for a
   constant but nonzero acceleration?

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Another Quiz

• Match v(t) to a(t)

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Relationship Between Acceleration and Velocity
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Kinematic Equations

• For uniform acceleration

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Graphical Interpretation
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The Daytona 500

• What is the velocity of the race car after it has
  traveled 100 feet if a5.00 m/s2 ?

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Acceleration due to Gravity Free Fall

• Symbolized by g
• g 9.80 m/s2
• When estimating, use g 10 m/s2
• g is always directed downward
• toward the center of the earth
• Ignoring air resistance and assuming g doesnt
  vary with altitude over short vertical distances,
  free fall is constantly accelerated motion

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Free Fall Problems