Introduction to Kinematics in One Dimension

1
Introduction to Kinematics in One Dimension

• Description of how an object moves
• Kinematic quantities
• Elapsed Time
• Position and Displacement
• Velocity and Speed
• Acceleration (dealt with at a later time)
• Motion is confined to a line.
• The object may move in either direction along the
  line. It may even change directions as it moves
  along the line.
• The object may never occupy a position that is
  not on the line.

2
Elapsed Time (?t)

• Elapsed time is the amount of time that passes
  from the beginning of an event (ti) until the end
  of the event (tf).
• Mathematically, ?t tf ti
• Units of time can be hours, minutes, days, etc.
  The SI unit of time is seconds (s).
• Note Think of time as being measured by a
  stopwatch, not by a clock. The beginning of the
  event could occur at 0.0 seconds but it could
  just as easily occur at some other positive time.
  We do not usually consider negative times.

3
Position (x)

• The magnitude (absolute value) of the position
  tells how far an object is located from some
  chosen reference point (origin).
• The sign ( or -) of the position tells the
  direction of the position of the object from the
  origin. One direction is chosen as the positive
  direction and the opposite direction becomes the
  negative direction.
• Units of position can be meters, centimeters,
  kilometers, feet, miles, etc. The SI unit of
  position is meters (m).
• EXAMPLES
• An object moves along a line that is oriented
  horizontally in the east-west direction and east
  is chosen as the positive direction. A position
  of 5 kilometers means that the object is located
  5 kilometers east of the origin.
• An object moves along a line that is oriented
  vertically and down is chosen as the positive
  direction. A position of -3 meters means that
  the object is located 3 meters above the origin.

4
Displacement (?x)

• Distance and direction of the final position (xf)
  of an object from its initial position (xi)
• Positions of the object at times between the
  initial and final times are irrelevant
• Mathematically, ?x xf xi
• Units of displacement are the same as units of
  position. The SI unit of displacement is meters
  (m).
• EXAMPLE
• An object moves along a horizontal line that is
  oriented in the north-south direction and north
  is chosen as the positive direction. The initial
  position of the object is 4.0 meters south of the
  origin and the final position is 3.0 meters north
  of the origin. What is the displacement of the
  object?
• Solution ?x xf xi 4.0 m (-3.0 m) 7.0
  m. The objects displacement is 7.0 m north.
  This result agrees with our intuition and does
  not depend on how the object moved between its
  initial and final positions.

5
Velocity (v)

• Average velocity (vavg) is defined as the
  displacement of an object divided by the elapsed
  time. A time interval must be identified when
  dealing with average velocity.
• Mathematically, vavg ?x/?t
• Instantaneous velocity (v) is the velocity of an
  object at one point in time. It is the average
  velocity of an object for a very small time
  interval (approaches zero).
• Units of velocity can be any unit of displacement
  divided by any unit of elapsed time. The SI unit
  of velocity is meters/second (m/s)

6
Speed

• Average speed is the distance an object travels
  divided by the elapsed time. As with average
  velocity, a time interval must be identified.
• Instantaneous speed is the magnitude (absolute
  value) of the instantaneous velocity.
• Direction is not a component of speed. Speed is
  always a positive value.
• Units of speed are the same as the units of
  velocity. The SI unit is m/s.
• EXAMPLES
• An object moves along a horizontal line that is
  oriented in the east-west direction with east as
  the positive direction. If the velocity of the
  object is 8 m/s it means that the object is
  traveling eastward at a speed of 8 m/s.
• Again, an object moves along a horizontal line
  that is oriented in the east-west direction with
  east as the positive direction. If the velocity
  of the object is -8 m/s it means that the object
  is traveling westward at a speed of 8 m/s.
• Note that in both examples, the speed of the
  object is 8 m/s, which is also the absolute value
  of the reported velocity.

7
(No Transcript)
8
(No Transcript)
9
Finding Velocity from Position vs. Time Graphs

• Instantaneous velocity is the slope of the
  position vs. time graph at the particular instant.