Chapter2_2_5

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Review and Announcements
• Tatiana Brusentsova is the Teaching
Assistant/Grader.
• My office hours will take place in Room
402 of the Physics Department.
• Make sure you are using WebAssign by
the end of the week! Homework #1 due
Monday.
Chapter 2: One-Dimensional Kinematics
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Outline
2-1 Position, Distance, and Displacement
2-2 Average Speed and Velocity
2-3 Instantaneous Velocity
2-4 Acceleration
2-5 Motion with Constant Acceleration
2-6 Applications of the Equations of Motion
2-7 Freely Falling Objects
Major Concepts
• Position, distance and displacement
• Speed and velocity
– Average
– Instantaneous
– Constant
• Acceleration
– Average
– Instantaneous
– Constant
• Graphs of position versus time, velocity versus time, and
acceleration versus time
• Equations of motion with constant acceleration
• Free fall
Warning Areas:
Speed vs. Velocity
Distance vs. Displacement
Constant Velocity vs. Constant Acceleration
Distance and displacement
• Displacement is the net change in position
from beginning to end of a journey
• Distance is the total amount of change in
position, including re-tracing your steps on
the journey.
Physics uses common terms in technical ways.
Figure 2-2
One-Dimensional Coordinates
Try some examples…
Speed and Velocity
• Speed is the distance traveled in a
period of time. It is a “scalar” (number
only).
• Velocity is the displacement in a period
of time. It is a “vector” (number and
direction).
Distance and displacement
What is the displacement at 1s, 2s, 3s, 4s?
What is the distance traveled at 1, 2, 3, 4s?
What is the average speed?
1. Greater than 40 mph.
2. Less than 40 mph.
3. Equal to 40 mph.
What is the average speed?
1.
2.
3.
Greater than 40 mph.
Less than 40 mph.
Equal to 40 mph.
X
Vavg 
T
T  T1  T2
X1
T1 
V1
Etc.
Problem solving:
-draw a picture
-label all quantities
-identify “unknown”
-write down relationships
(formulas), working
backwards from unkown to
known
-find a formula for the
unknown
-plug in the numbers
Example 2-2
Sprint Training
Compare the average speed, and average velocity.
Figure 2-4
Motion Along the X Axis Represented with an x-Versus-t Graph
Figure 2-5a
Average Velocity on an x-Versus-t Graph
Figure 2-6
Constant Velocity on an x-Versus-t Graph
Figure 2-7
Instantaneous Velocity
Figure 2-8
Graphical Interpretation of Average and Instantaneous Velocity
Our first formula!
If the velocity is constant, then the
average velocity is the same as the
instantaneous velocity.
X
V
T
X  X  X 0
VAVG 
T  T  T0  T
V
X  X0
T
Rearranging:
X  X 0  VT
Acceleration
• Acceleration is the change in velocity
per unit time
• The average acceleration is the change
in velocity per change in time. It is a
vector quantity.
Figure 2-9
v-Versus-t Plots for Motion with Constant Acceleration
Our second formula!
For constant acceleration…
a
v v  v0 v  v0


t t  t0
t
at  v  v0
v  v0  at
Velocity versus
time produces a
straight line graph,
if acceleration is
constant.
Figure 2-10
Graphical Interpretation of Average and Instantaneous
Acceleration
Example 2-3
An Accelerating Train
Cars Accelerating or Decelerating
which picture matches which graph?
1
2
3
4
Figure 2-13a
The Average Velocity
Definition: change in velocity
divided by time.
Special case: Constant
acceleration
Example 2-6
Put the Pedal to the Metal
Figure 2-16
Velocity as a Function of Position for the Ranger in Example 2-8
Notice that ½ the speed is lost in last ¼ of stopping distance.
CONSTANT DECELERATION
Example 2-9a
Catching a Speeder
Q: How many mph?
Table 2-4
Constant-Acceleration Equations of Motion
Variables Related
Equation
Number
Velocity, time,
acceleration
v = v0 + at
2-7
Initial, final, and
average velocity
vav = ½(v0 + v)
2-9
Position, time,
velocity
x = x0 + ½(v0 + v)t
2-10
Position, time,
acceleration
x = x0 + v0t + ½ at2
2-11
Velocity, position,
acceleration
v2 = v02 + 2a(x – x0) = v02 + 2ax
2-12
Figure 2-22
Problem 2-3
Figure 2-25
Problem 2-17
Figure 2-26
Problem 2-21
Find the average velocity for
each segment of the “walk”,
and for the total “walk”.
Now, compare DISPLACEMENT and DISTANCE.
Compare, average VELOCITY and SPEED.
Figure 2-28
Problem 2-32
What is the average acceleration
for each segment, what is the
average acceleration for the whole
motorcycle ride?
Figure 2-29
Problem 2-33
CAREFUL!
What is the displacement
for each segment of the
graph shown?
Problem solving:
1. Draw a picture (given)
2. What are they asking for?
3. What is given?
4. What are the mathematical relationships?
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