UC AIT AP Physics C: Mechanics

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UC AIT AP Physics C Mechanics Summer Assignment
2009-2010 The purpose of this summer assignments
is to give you a head start on the introductory
material in your AP Physics C course.  AP Physics
is a college level course and is above the level
of Physics 1 Honors which you have already
taken.  Your teacher is here to help you and
guide you through this process of learning, but
to a large degree you will be responsible for
developing an understanding through your own
efforts (this is a skill you NEED to develop for
college). Summer assignment will be collected
when you return to school and graded as your
first quiz grade for AP Physics C Mechanics 1.
Search the internet for a few sources on
Physics-mechanics, kinematics, calculus and
kinematics, etc. The sites you find may come in
handy during the coming school year. You can also
refer to the notes on my teacher website here
http//www.ucvts.tec.nj.us/ucvts/Staff/Timothy20L
averick/AP20Physics20C20Mechanics/Lecture20Not
es-assignment20materials/1D20Kinematics20SJ620
Ch202.ppt/_top 2. do the following problems on
notebook paper (show your work). You will need to
use some basic Calculus (derivatives) in solving
a few of the problems. 1. The position of a
pinewood derby car was observed at various times
the results are summarized in the following
table. Find the average velocity of the car for
(a) the first second, (b) the last 3 s, and (c)
the entire period of observation.

• (a) Sand dunes in a desert move over time as sand
  is swept up the windward side to settle in the
  lee side. Such walking dunes have been known
  to walk 20 feet in a year and can travel as much
  as 100 feet per year in particularly windy times.
  Calculate the average speed in each case in m/s.
  (b) Fingernails grow at the rate of drifting
  continents, on the order of 10 mm/yr.
  Approximately how long did it take for North
  America to separate from Europe, a distance of
  about 3 000 mi?
• 3. The position versus time for a certain
  particle moving along the x axis is shown in the
  figure below. Find the average velocity in the
  time intervals (a) 0 to 2 s, (b) 0 to 4 s, (c) 2
  s to 4 s, (d) 4 s to 7 s, (e) 0 to 8 s.

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4. A particle moves according to the equation x
10t2 where x is in meters and t is in seconds.
(a) Find the average velocity for the time
interval from 2.00 s to 3.00 s. (b) Find the
average velocity for the time interval from 2.00
to 2.10 s. 5. A person walks
first at a constant speed of 5.00 m/s along a
straight line from point A to point B and then
back along the line from B to A at a constant
speed of 3.00 m/s. What is (a) her average speed
over the entire trip? (b) her average velocity
over the entire trip? 6. The position of
a particle moving along the x axis varies in time
according to the expression x 3t2, where x is
in meters and t is in seconds. Evaluate its
position (a) at t 3.00 s and (b) at 3.00 s
?t. (c) Evaluate the limit of ?x/?t as ?t
approaches zero, to find the velocity at t
3.00 s.
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7. A position-time graph for a particle moving
along the x axis is shown in the figure at the
right. (a) Find the average velocity in the time
interval t 1.50 s to t 4.00 s. (b) Determine
the instantaneous velocity at t 2.00 s by
measuring the slope of the tangent line shown in
the graph. (c) At what value of t is the
velocity zero?
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Kinematics

• Describes motion while ignoring the agents that
  caused the motion
• For now, will consider motion in one dimension
• Along a straight line
• Will use the particle model
• A particle is a point-like object, has mass but
  infinitesimal size

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Position

• Defined in terms of a frame of reference
• One dimensional, so generally the x- or y-axis
• The objects position is its location with
  respect to the frame of reference

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Position-Time Graph

• The position-time graph shows the motion of the
  particle (car)
• The smooth curve is a guess as to what happened
  between the data points

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Displacement

• Defined as the change in position during some
  time interval
• Represented as ?x
• ?x xf - xi
• SI units are meters (m) ?x can be positive or
  negative
• Different than distance (which is the length of a
  path followed by a particle)

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Vectors and Scalars

• Vector quantities need both magnitude (size or
  numerical value) and direction to completely
  describe them
• Will use and signs to indicate vector
  directions
• Scalar quantities are completely described by
  magnitude only

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Average Velocity

• The average velocity is rate at which the
  displacement occurs
• The dimensions are length / time L/T
• The SI units are m/s
• Is also the slope of the line in the position
  time graph

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Average Speed

• Speed is a scalar quantity
• same units as velocity
• total distance / total time
• The average speed is not (necessarily) the
  magnitude of the average velocity

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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, equations

• The general equation for instantaneous velocity
  is
• The instantaneous velocity can be positive,
  negative, or zero

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Instantaneous Velocity, graph

• The instantaneous velocity is the slope of the
  line tangent to the x vs. t curve
• This would be the green line
• The blue lines show that as ?t gets smaller, they
  approach the green line

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Instantaneous Speed

• The instantaneous speed is the magnitude of the
  instantaneous velocity
• Remember that the average speed is not the
  magnitude of the average velocity

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Average Acceleration

• Acceleration is the rate of change of the
  velocity
• Dimensions are L/T2
• SI units are m/s²

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Instantaneous Acceleration

• The instantaneous acceleration is the limit of
  the average acceleration as ?t approaches 0

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Instantaneous Acceleration -- graph

• The slope of the velocity vs. time graph is the
  acceleration
• The green line represents the instantaneous
  acceleration
• The blue line is the average acceleration

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Acceleration and Velocity, 1

• When an objects velocity and acceleration are in
  the same direction, the object is speeding up
• When an objects velocity and acceleration are in
  the opposite direction, the object is slowing
  down

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Acceleration and Velocity, 2

• The car is moving with constant positive velocity
  (shown by red arrows maintaining the same size)
• Acceleration equals zero

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Acceleration and Velocity, 3

• Velocity and acceleration are in the same
  direction
• Acceleration is uniform (blue arrows maintain the
  same length)
• Velocity is increasing (red arrows are getting
  longer)
• This shows positive acceleration and positive
  velocity

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Acceleration and Velocity, 4

• Acceleration and velocity are in opposite
  directions
• Acceleration is uniform (blue arrows maintain the
  same length)
• Velocity is decreasing (red arrows are getting
  shorter)
• Positive velocity and negative acceleration

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Kinematic Equations -- summary
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Kinematic Equations

• The kinematic equations may be used to solve any
  problem involving one-dimensional motion with a
  constant acceleration
• You may need to use two of the equations to solve
  one problem
• Many times there is more than one way to solve a
  problem

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Graphical Look at Motion displacement time
curve

• The slope of the curve is the velocity
• The curved line indicates the velocity is
  changing
• Therefore, there is an acceleration

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Graphical Look at Motion velocity time curve

• The slope gives the acceleration
• The straight line indicates a constant
  acceleration

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Graphical Look at Motion acceleration time
curve

• The zero slope indicates a constant acceleration

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Motion Equations from Calculus

• Displacement equals the area under the velocity
  time curve
• The limit of the sum is a definite integral

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Kinematic Equations General Calculus Form
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Kinematic Equations Calculus Form with Constant
Acceleration

• The integration form of vf vi gives
• The integration form of xf xi gives