AP Physics Mechanics for Physicists and Engineers Agenda for Today

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AP Physics Mechanics for Physicists and
EngineersAgenda for Today

• 1-D Kinematics (review).
• Average instantaneous velocity and acceleration
• Motion with constant acceleration
• Introduction to calculus applications
• derivatives and slopes
• Integrals and area

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Kinematics Problems

• 1-D Kinematics
• Average instantaneous velocity (Chapter2
  1,4,5,11-13,15-17) and acceleration (18,21)
• Motion with constant acceleration(23,24,27,31,35,3
  7,39,40-1,43)
• Free Fall (44,47,49,51,53,56,61,63)
• Motion Graphs (66,67,69,70)
• Review Phun!!

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Kinematics

• Location and motion of objects is described using
  Kinematic Variables
• Some examples of kinematic variables.
• position r vector
• velocity v vector
• Kinematic Variables
• Measured with respect to a reference frame. (x-y
  axis)
• Measured using coordinates (having units).
• Many kinematic variables are Vectors, which means
  they have a direction as well as a magnitude.
• Vectors denoted by boldface V or arrow

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Motion in 1 dimension
See text 2-1

• In general, position at time t1 is usually
  denoted r(t1).
• In 1-D, we usually write position as x(t1 ).
• Since its in 1-D, all we need to indicate
  direction is or ?.
• Displacement in a time ?t t2 - t1 is
  ?x x(t2 ) - x(t1 ) x2 - x1

x
some particles trajectoryin 1-D
x2
??x
x1
t
t1
t2
??t
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1-D kinematics
See text 2-1

• Velocity v is the rate of change of position
• Average velocity vav in the time ??t t2 - t1
  is

x
trajectory
x2
??x
Vav slope of line connecting x1 and x2.
x1
t
t1
t2
??t
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1-D kinematics...
See text 2-2

• Instantaneous velocity v is defined as

x
so V(t2 ) slope of line tangent to path at t2.
x2
??x
x1
t
t1
t2
??t
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1-D kinematics...
See text 2-3

• Acceleration a is the rate of change of
  velocity
• Average acceleration aav in the time ??t t2
  - t1 is

• And instantaneous acceleration a is defined as

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Recap

• If the position x is known as a function of time,
  then we can find both velocity v and acceleration
  a as a function of time!

x
t
v
t
a
t
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More 1-D kinematics

• We saw that v ?x / ?t
• so therefore ?x v ?t ( i.e. 60 mi/hr x 2 hr
  120 mi )
• In calculus language we would write dx v dt,
  which we can integrate to obtain

• Graphically, this is adding up lots of small
  rectangles

v(t)

...
displacement
t
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1-D Motion with constant acceleration
See text 2-4

• High-school calculus
• Also recall that
• Since a is constant, we can integrate this using
  the above rule to find
• Similarly, since we can
  integrate again to get

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Recap
See text Table 2-1 (p. 33)

• So for constant acceleration we find

x
t
v

• From which we can derive

t
a
t
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Problem 1

• A car traveling with an initial velocity vo. At
  t 0, the driver puts on the brakes, which slows
  the car at a rate of ab

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Problem 1...

• A car traveling with an initial velocity vo. At
  t 0, the driver puts on the brakes, which slows
  the car at a rate of ab. At what time tf does
  the car stop, and how much farther xf does it
  travel ??

vo
ab
x 0, t 0
v 0
x xf , t tf
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Problem 1...

• Above, we derived (a)
  (b)
• Realize that a -ab
• Using (b), realizing that v 0 at t tf
• find 0 v0 - ab tf or tf vo /af
• Plugging this result into (a) we find the
  stopping distance

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Problem 1...

• So we found that
• Suppose that vo 65 mi/hr x .45 m/s / mi/hr
  29 m/s
• Suppose also that ab g 9.8 m/s2.
• Find that tf 3 s and xf 43 m

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Tips

• Read !
• Before you start work on a problem, read the
  problem statement thoroughly. Make sure you
  understand what information in given, what is
  asked for, and the meaning of all the terms used
  in stating the problem.
• Watch your units !
• Always check the units of your answer, and carry
  the units along with your numbers during the
  calculation.
• Understand the limits !
• Many equations we use are special cases of more
  general laws. Understanding how they are derived
  will help you recognize their limitations (for
  example, constant acceleration).

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Recap of kinematics lectures

• 1-D Kinematics
• Average instantaneous velocity (Chapter3-
  1,3,7,9,11) and and acceleration
• Motion Graphs (14,15,17,19)
• Motion with constant acceleration(Ch3
  21,23,27,29,31,35,37 41)
• Free Fall (Ch3-41,43,47,49,51,52)
• Review Phun!! (67,69,70 )