Ch 2. Motion in a Straight Line Definitions 1. Kinematics - Motion Kinetic Energy - Energy associated with motion 2. Motion in physics is broken down into categories a.) Translational Motion - motion such that an object moves from one

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Ch 2. Motion in a Straight Line
Definitions1. Kinematics - Motion Kinetic
Energy - Energy associated with motion2. Motion
in physics is broken down into categories a.)
Translational Motion - motion such that an
object moves from one position to another along a
straight line. b.) Rotational Motion -
motion such that an object moves from one
position to another along a circular path. c.)
Vibrational Motion - motion such that an object
moves back and forth in some type of periodicity.
One Dimensional (x-axis only)
Motion in 3-D space can be complicated
Straight Line
Spinning
Up and Back
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• Example Diatomic Molecule Moving Through Space.

f
Net Translation
i
X - Dir
Note In this chapter all objects are going to
be considered POINT PARTICLES No Spatial Extent
No Rotations No Vibrations
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• Speed
• Speed - How fast an object is moving regardless
  of what direction it is moving.

Equality by Definition
Example 1 Traveling from your parking space at
Conestoga to New York City and back to Conestoga.
Find your average speed for the round trip.
One way travel 130 mi. Total Distance Traveled
260 mi. Total time elapsed 5.2 hrs. or (5 hrs
12 min)
Speed Calculations are EASY Always distance / time
Round Trip Average Speed
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• Displacement - Change in position (straight line
  distance with direction)
• Must specify a coordinate system.

Example Cartesian coordinate system
up
back
Mathematical Notation for Direction
? Delta
Delta x is the displacement or change in the x
position
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Average Velocity
Avg. Velocity - How fast an object is moving and
in what direction it is moving.

Equality by Definition
?
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Notation for Displacement Velocity

• x hat, and has a value of one. The sole
  purpose of is to indicate the direction
• Example Problem
• A particle initially at position x 5 m at time
  t 2 s moves to position x -2 m and arrives at
  time t 4 s.
• a.) Find the displacement of the particle.
• b.) Find the average speed and velocity of the
  particle.

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Example Problem 1 revisited Example 1. Traveling
from your parking space at Conestoga to New York
City and back to Conestoga. The straight line
distance from Conestoga to Y is 97 mi.
One way travel 130 mi. Total Distance Traveled
260 mi. Travel time Con. to NY 2.6
hrs. Travel time NY to Con. 2.6 hrs.
a.) What was the avg speed from Conestoga to NY?
b.) What was the avg velocity from Conestoga to
NY?
c.) What was the avg speed for the round trip?
d.) What was the avg velocity for the round trip?
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Scalar vs. Vector Quantities Scalar - Quantity
that has magnitude only. - Mass - Speed -
Length - Energy Vector - A quantity that has
both magnitude and direction. - Position -
Acceleration - Velocity - Forces
Example Length vs. Position
Scalar
Vector
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Concepts Check The Negatives
Q. Can speed be negative?
A. NO! The least speed an object can have is
zero it is at rest

• Q. Can velocity be negative?

Q. Can distance be negative?
A. NO! The least distance an object can move is
zero it is at rest
Q. Can displacement be negative?
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Position vs. Time Graph
Both of these movements describe an object moving
in one dimension along the x-axis! NOT up and to
the right!
x Y1 Y2
Time (s) Position (m) Position (m)
0 0 0
1 1 5
2 4 10
3 9 15
4 16 20
5 25 25
Movement 1
Movement 2
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Position vs. Time Graph for a Complete Trip
x y
Time (s) Position (m)
0 0
10 200
20 200
25 150
45 -100
60 0
Find the average velocity as the object moves
from a.) A to B b.) B to C c.) C to D
d.) A to E
Slope of the secant line is vavg
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Velocity vs. Time (Constant Velocity)
run
Dx
rise
Area
Slope
?t base
v height
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Velocity vs. Time Graph for a Complete Trip
Velocity vs. Time Graph for a Complete Trip
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Instantaneous Velocity recall
(Average velocity)
?t 1.5 sec
A.
Consider the function x(t)
?t 0.2 sec
B.
?
?
?
The instantaneous velocity at the time t ti is
the limiting value we get by letting the upper
value of the tf approach ti. Mathematically
this is expressed as The velocity function
is the time derivative of the position function
. Differentiation (Calculus)
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Acceleration When the instantaneous velocity of a
particle is changing with time, the particle is
accelerating
(Average Acceleration)
Units
Example If a particle is moving with a velocity
in the x-direction given by
a.) What is the average acceleration over the
time interval
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Example Instantaneous Acceleration
a.) Find aavg. over the time interval 5 ? t ? 8
b.) What is the acceleration at time t 6 s ?
c.) What is the acceleration when the
velocity of the particle is zero?
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Positive and Negative Accelerations
v(m/s)
D
C
t (s)
E
B
A
F
A?B B?C C?D D?E E?F
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Special Case Constant Acceleration
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Solving for the 3rd constant acceleration
equation Solve equation 1 for t and substitute t
into equation 2 to get the following equation.
3.


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FREE-FALL ACCELERATION (9.8 m/s2 32
ft/s2) Consider a ball is thrown straight up. It
is in Free Fall the moment it leaves you
hand. Plot y(t) vs. t for the example above.

Plot v(t) vs. t

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FINAL NOTES ON CH 2. Remember , when going
between the following graphs

• Problem Solving with the constant acceleration
  equations
• Write down all three equations in the margin
• a ? 9.8 m/s2 for free fall problems
• Analyze the problem in terms of initial and final
  sections.