4.4 Average Value and Physics Connections

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4.4 Average Valueand Physics Connections
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Average Value of a Function

• The average value of a continuous function f(x)
  on some interval from a to b is given by the
  equation
• It looks like an average, doesnt it.

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Example

• Find the average value of the function
• on the interval from 1 to
  5

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Physics

• The relationship between velocity v(t),
  acceleration a(t) and position x(t) is this
• To use this we need to understand 2 definitions.

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Net Change vs Total Distance

• If you drive to Starbucks then back (and park in
  the very same parking place) your net change is
  0, right?
• But, the odometer value has changed. That is,
  the total distance traveled is NOT zero. This
  works in physics when a particle is moving along
  a straight line path (typical situation)

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Net Change

• Net Change displacement net change in the
  position of a body moving along a line from a to
  b.
• Mathematically
• where some distances will be positive (up or
  forward) while others will be negative (down
  or backward). The Net change is the result of
  these movements.

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Total Distance

• Total Distance the sum of all the distances.
  Therefore, you will need to know where it changes
  from to directionally, and add the absolute
  values of all these.

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WHAT?

• Imagine. A particle moves forward 10 m then
  backwards 7 m.
• Net Change? 3 m
• Total Distance? 17 m

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Well, how do I do that?

• Often, a sketch of the velocity is a very good
  idea. This will quickly identify where the
  distance is positive and where it is negative.
  Take the absolute value of anything negative and
  add all of these numbers.

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Examples

• 1. Given that a particle travels according to
  the equation
• Find the net change AND the total distance
  traveled by the particle.
• Homework Worksheet