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Introduction to Kinematics

Kinematics is the branch of Mechanics that deals with the description of the motion of objects, without consideration of what causes motion.

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Two types of physical quantities:

  • Scalars
    • Identified by a single number
    • Examples:
      • Temperature
      • Mass
      • Distance traveled
    • May still have + / – associated with it.
  • Vectors
    • Identified by magnitude (number) AND direction
    • We’ll see examples in this presentation.��
    • Direction may be given with + / –.

CAUTION

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Speed (a scalar quantity)

  • When something is in motion, its position changes with time.
  • Both length and time are therefore important quantities in describing motion

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Displacement (a vector quantity)

  • Definition: the straight-line distance between two points, along with the direction directly from the starting point to the final position.
  • Can be + or - with the signs indicating the direction along the coordinate axis.
  • The displacement between x1 and x2 is:

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Velocity (a vector quantity)

 

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BE CAREFUL

  • There are many types of velocities:
    • Average velocity
    • Instantaneous velocity
      • Initial velocity
      • Final velocity
  • Example:
    • Driving to school. 4 miles away. Takes me about 10 minutes.
    • Average velocity is 24mph.
    • Does that mean I’m going 24mph all the time?

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Example #1

  • A woman jogs once around a 400m track in 80 seconds.
  • Find:
    • Her average speed
    • Her average velocity

5 m/s

0 m/s

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Example #2

  • An energetic bug travels on a line in the path shown below in 10s.���
  • Find
    • Distance traveled
    • Displacement
    • Average speed
    • Average velocity

35m

45m

80 m

-10 m

8 m/s

-1 m/s