from Chapter 2

1
from Chapter 2
Phys 110Element of PhysicsLecture 02

• Velocity and Speed
• in One Dimension

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Dynamics

• The branch of physics involving the motion of an
  object and the relationship between that motion
  and other physics concepts
• Kinematics is a part of dynamics
• In kinematics, you are interested in the
  description of motion
• Not concerned with the cause of the motion

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Quantities in Motion

• Any motion involves three concepts
• Displacement
• Velocity
• Acceleration
• These concepts can be used to study objects in
  motion

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Brief History of Motion

• Sumaria and Egypt
• Mainly motion of heavenly bodies
• Greeks
• Also to understand the motion of heavenly bodies
• Systematic and detailed studies
• Geocentric model

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Modern Ideas of Motion

• Copernicus
• Developed the heliocentric system
• Galileo
• Made astronomical observations with a telescope
• Experimental evidence for description of motion
• Quantitative study of motion

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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
• xf stands for final and xi stands for initial
• May be represented as ?y, if vertical
• Units are meters (m) in SI, centimeters (cm) in
  cgs or feet (ft) in US Customary

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Displacements
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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 and an arrow
  over the letter
• or sign is sufficient for 1-dim
• Scalar quantities are completely described by
  magnitude only

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Can you identify other Vector and Scalar
Quantities?

• Scalars Vectors
  .

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Displacement Isnt Distance

• The displacement of an object is not the same as
  the distance it travels
• Example Throw a ball straight up and then catch
  it at the same point you released it
• The distance is twice the height
• The displacement is zero

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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

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Speed, cont

• Average speed totally ignores any variations in
  the objects actual motion during the trip
• The total distance and the total time are all
  that is important
• SI units are m/s

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Velocity

• It takes time for an object to undergo a
  displacement
• The average velocity is rate at which the
  displacement occurs
• generally use a time interval, so let ti 0

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Velocity continued

• Direction will be the same as the direction of
  the displacement (time interval is always
  positive)
• or - is sufficient
• Units of velocity are m/s (SI), cm/s (cgs) or
  ft/s (US Cust.)
• Other units may be given in a problem, but
  generally will need to be converted to these

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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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Graphical Interpretation of Velocity

• Velocity can be determined from a position-time
  graph
• Average velocity equals the slope of the line
  joining the initial and final positions
• An object moving with a constant velocity will
  have a graph that is a straight line

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Average Velocity, Constant

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

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Average Velocity, Non Constant

• The motion is non-constant 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, or as the
  time interval approaches zero
• The instantaneous velocity indicates what is
  happening at every point of time

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Instantaneous Velocity on a Graph

• The slope of the line tangent to the
  position-vs.-time graph is defined to be the
  instantaneous velocity at that time
• The instantaneous speed is defined as the
  magnitude of the instantaneous velocity

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Uniform Velocity

• Uniform velocity is constant velocity
• The instantaneous velocities are always the same
• All the instantaneous velocities will also equal
  the average velocity

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Example Problem 1

• A person travels by car from one city to another
  with different constant speeds.
• 30.0 minutes at 80.0 km/hr
• 12.0 minutes at 100. km/hr
• 45.0 minutes at 40.0 km/hr
• 15.0 minutes eating lunch and buying gas.
• What is the persons average speed?
• What is the total distance traveled?

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Example Problem 2

• The distance of dropped object was measured
  over a time period of 5 seconds and is given to
  the right.
• What can we determine about the objects speed
  and velocity?

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Example Problem 2 cont.

• How do you find the average speed for each
  interval?
• How do you find the average speed for the
  entire 5 seconds?

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Homework Assignment 02

• Chapter 2, Problem 3 on page 48
• Chapter 2, Problem 7 on page 48