Honors Physics Mechanics for Physicists and Engineers Agenda for Today

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Honors Physics Mechanics for Physicists and
EngineersAgenda for Today

• Advice
• 1-D Kinematics
• Average instantaneous velocity and acceleration
• Motion with constant acceleration
• Freefall

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Kinematics Objectives

• Define average and instantaneous velocity
• Caluclate kinematic quantities using equations
• interpret and plot position -time graphs
• be able to determine and describe the meaning of
  the slope of a position-time graph

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Kinematics

• Location and motion of objects is described using
  Kinematic Variables
• Some examples of kinematic variables.
• position r vector, (d,x,y,z)
• velocity v vector
• acceleration a 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 above the
  variable

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Motion

• Position Separation between an object and a
  reference point (Just a point)
• Distance Separation between two objects
• Displacement of an object is the distance between
  its final position df and its initial position
  d i (d f - di)? d
• Scalar Quantity that can be described by a
  magnitude(strength) only
• Distance, temperature, pressure etc..
• Vector A quantity that can be described by both
  a magnitude and direction
• Force, displacement, torque etc.

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Speed and Velocity

• Speed describes the rate at which an object
  moves. Distance traveled per unit of time.
• Velocity describes an objects speed and
  direction.
• Approximate units of speed

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Motion in 1 dimension

• In general, position at time t1 is usually
  denoted d, r(t1) or x(t1)
• In 1-D, we usually write position as x(t1 ) but
  for this level well use d
• Since its in 1-D, all we need to indicate
  direction is or ?.
• Displacement in a time ?t t2 - t1 is
  ?x x2 - x1 d2 -d1

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

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

x
trajectory
d2
??x
Vav slope of line connecting x1 and x2.
d1
t
t1
t2
??t
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1-D kinematics...

• Instantaneous velocity v is defined as the
  velocity at an instant of time (??t 0)
• Slope formula becomes undefined at ??t 0

x
so V(t2 ) slope of line tangent to path at t2.
x2
??x
x1

• Calculus Notation

t
t1
t2
??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 )
• See text 3.2
• 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 kinematics...

• 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
  asThe acceleration when ??t 0 . Same problem
  as instantaneous velocity. Slope equals line
  tangent to path of velocity vs time graph.

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Problem Solving

• 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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IV. Displacement during acceleration.

• You accelerate from 0 m/s to 30 m/s in 3
  seconds, how far did you travel?
• What if a car initially at 10 m/s, accelerates at
  a rate of 5 m/s2 for 7 seconds. How far does it
  move?
• df1/2at2 vit di
• C. An airplane must reach a speed of 71 m/s for a
  successful takeoff. What must be the rate of
  acceleration if the runway is 1.0 km long?
• d (vf2 - vi2) /2a

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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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Recap

• So for constant acceleration we find

x
t
v

• From which we can derive

t
a
t
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IV. Acceleration due to gravity

• The acceleration of a freely falling object is
  9.8 m/s2 (32 ft/s2) towards the earth.
• The farther away from the earths center, the
  smaller the value of the acceleration due to
  gravity. For activities near the surface of the
  earth (within 5-6 km or more) we will assume
  g9.8 m/s2 (10 m/s2).
• Neglecting air resistance, an object has the
  same acceleration on the way up as it does on the
  way down.
• Use the same equations of motion but substitute
  the value of g for acceleration a.

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Recap of kinematics lectures

• Measurement and Units (Chapter 1)
• Systems of units
• Converting between systems of units
• Dimensional Analysis
• 1-D Kinematics
• Average instantaneous velocity and and
  acceleration
• Motion with constant acceleration

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