Physics 121: Fundamentals of Physics I

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Physics 121Fundamentals of Physics I

• September 15, 2006

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Example Problem

• A ball thrown by a pitcher on a womens softball
  team is timed at 65.0 mph. The distance from the
  pitching rubber to home plate is 43.0 ft. In
  major league baseball the corresponding distance
  is 60.5 ft. If the batter in the softball game
  and the batter in the baseball game are to have
  equal times to react to the pitch, with what
  speed must the baseball be thrown?

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Average Acceleration

• We need to keep track not only of the fact that
  something is moving but how that motion is
  changing.
• Define the average acceleration by

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Average Acceleration
Note!
Figure 2.9
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Instantaneous acceleration

• Sometimes (often) an object will move so that
  sometimes it speeds up or slows down at different
  rates.
• We want to be able to describe this change in
  motion also.
• If we consider small enough time intervals, the
  change in velocity will look uniform for a
  little while at least.

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Technical term alert!

• Note that in physics we use the term
  acceleration in a technically defined way
• acceleration changing velocity
• The object may be speeding up or slowing down or
  keeping the same speed and changing direction.
  We still say it is accelerating.
• In common speech acceleration speeding
  up,deceleration slowing down, and
  turningchanging direction.
• How many (physics) accelerators are there on
  your car?

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Equations of Motion

• There are a LOT of equations in the book for
  describing one-dimensional motion with constant
  acceleration
• Most of them involve certain special cases or are
  just the same equation written in different ways
• I dont expect you to just memorize the equations
• Unless you really understand when they are
  applicable, they can lead you in to trouble!
• There are just two equations that we have used
  so far
• They are really definitions
• Everything else can be derived from them
• I think you will be better served in the long run
  if you really understand these definitions and
  then know how to derive on your own the other
  equations
• ALWAYS START FROM THE DEFINITIONS!

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Equations of Motion

• Definitions
• Average Velocity
• Average Acceleration
• Knowing and Understanding these two definitions
  is key
• Also, relationship between position, velocity,
  and acceleration vs. time graphs

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Equations of Motion

• Special Case 1 Constant Motion
• Constant Motion means velocity isnt changing
• Also means
• Speed isnt changing
• Direction isnt changing
• Acceleration is zero
• Velocity could be zero, but doesnt have to be
• Position vs. time straight line
• Velocity vs. time constant (flat) line
• Acceleration vs. time constant (flat) line at 0!
• Equations

If at ti0, xix0, then
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Equations of Motion

• Special Case 2 Constant Acceleration
• Acceleration isnt changing, but isnt
  necessarily zero
• Velocity IS changing
• Position IS changing
• Position vs. time Curved graph (parabola)
• Velocity vs. time Straight line
• Acceleration vs. time Flat (constant) line
• Equations

If at ti0, viv0, then
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Constant Acceleration (more)

• Equation for position vs. time
• Because the velocity is increasing or decreasing
  uniformly with time (straight line), the average
  velocity in a time interval will just be the
  average of the initial and final velocities

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Notes

• All of these derivations begin with our
  definitions of average velocity and average
  acceleration
• If you want to memorize these equations, you need
  to keep track of the special cases involved
• Constant velocity vs. constant acceleration
• Are you given initial velocity (v0) and initial
  position (x0)?
• Form of equation could be different if you are
  given final position and velocity
• If the initial position and/or velocity is zero,
  equations look different
• Just dont use that form unless these conditions
  are true!
• Not all motion begins at t0
• Bottom line I think you are better off learning
  how to derive these equations, and knowing what
  they mean
• Knowing what they mean means Does it make
  sense for your problem

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Example

• Look at Ch. 2, Prob. 37
• A car starts from rest and travels for 5.0 s with
  a uniform acceleration of 1.5 m/s2. The driver
  then applies the brakes, causing a uniform
  acceleration of -2.0 m/s2. If the brakes are
  applies for 3.0 s,
• How fast is the car going at the end of the
  braking period?
• How far has the car gone?