Transcript Chapter 2

Name
Period
Test Corrections: Ch. 1 – A or B
•
•
•
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Copy each question you missed. You do
not have to copy the graphs, but you are
welcome to do so if you like.
Do not copy the answers choices.
If a problem required you to do work, you
must show it on paper or reference your
scratch paper.
Write the answer choice and put a box
around it.
Ex. A. 300.0
Chapter 2
Representing Motion Notes
Time Interval
Time is a variable that we really have
very little control over. Therefore, it is
very important for us to be able to focus
in on a small section of time during a
problem. To find the time interval, we
look at the final time and the initial time.
t  t f  t i
Time Interval
t  t f  t i
• Find the time intervals:
• The runner sped up from 4.5s to 8.5s
• 8.5 - 4.5 = 4.0 seconds

• Class lasted from 10:31am to 11:25am
• 11:25 - 11:00 = 25 min
• 11:00 - 10:31 = 29 min
• 25 + 29 = 54 minutes
Helpful to use the
hour as a midway
point
Position-Time Graphs
The slope (rise over run) of a
position-time graph is equal to
speed.
Mouse in a Tunnel
4
3
2
1
0
-1
-2
-3
-4
Mouse Position
Position (cm)
40
20
0
0
2
4
6
-20
-40
Time (s)
8
10
12
Understanding the Graph
Mouse Position
Position (cm)
40
20
0
0
2
4
6
8
10
12
-20
-40
Time (s)
 From 0-2s, the mouse moves forward.
 From 2-4s, the mouse moves forward
but at a slower speed (smaller slope).
 From 4-6s, the mouse does not move
(speed and slope = 0cm/s).
Understanding the Graph
Mouse Position
Position (cm)
40
20
0
0
2
4
6
8
10
12
-20
-40
Time (s)
 From 6-8s, the mouse moves backward.
 From 8-10s, the mouse moves backward at a
faster speed (greater slope) and crosses the
origin.
 From 10-12s, the mouse moves forward again
ending back at the starting point (origin).
Homework Questions
Complete Graphing Handout
Textbook:
Page 39, #9, 11, 12
Page 41, #14-17
Journal #
Determine the speed of the
object represented in the
graph. Show all of your work.
The Speed Formula
 To calculate
speed, distance,
or time, we can
use the speed
formula.
d
v
t
The “Magic” Triangle
distance in
meters
speed in
m/s
time in
seconds
Steps to working ANY problem in physics
1.
2.
3.
4.
5.
6.
7.
8.
Check the units, convert if necessary
Count the sig figs in the problem
Sketch a picture and label it
Define the variables
Choose a formula
Calculate the answer
Check answer for sig figs and unit
Check answer for vector or scalar properties
Example 1
A dog runs 25 meters in 15
seconds. What was his speed?
Example 1
A dog runs 25 meters in 15
seconds. What was his speed?
d  25m
t  15s
v ?
d
v
t
25m
v
 1.7m /s
15s
Example 2
A ball is rolling at a constant
speed of 15 m/s. How long will
it take for the ball to roll 150m?
Example 2
A ball is rolling at a constant
speed of 15 m/s. How long will
it take for the ball to roll 150m?
d  150m
t ?
v  15m /s
d
t
v
150m
v
 10s
15m /s
Example 3
How far have you traveled if
you move at a constant speed
of 55mph for 4.0 hours?
Example 3
How far have you traveled if
you move at a constant speed
of 55mph for 4.0 hours?
d?
t  4.0hrs
v  55mph
d  vt
d  55mph  4.0h
d  220mi
Example 4- Mixed Units
 A car travels at a constant speed
of 10.0m/s for 2.0 hours. How far
did the car travel during that time?
Hint: Convert 2.0 hours to seconds
60min 60sec
time  2.0hrs 

 7200s
1hr
1min
d  vt  10.0m /s  7200s  7.2 10 m
4
Example 5-More Mixed
Units
 A boy jogs for 45 minutes and travels
2.0km. What was his average speed
in m/s?
Hint: Convert 45 minutes to seconds
and Convert 2.0 km to meters
60sec
time  45min 
 2700s
1min
distance  2.0km  2.0 10 3 m


d 2.0 10 3 m
v 
 0.74m /s
t
2700s
When does direction
matter?
In physics, all numbers are either
scalar or vector quantities.
• Scalar - Have a magnitude and a
unit, but do not indicate direction
Ex.) distance = 5m, time = 10 s, etc.
• Vector - Have magnitude, a unit, and
direction
Ex.) displacement = 3m North, velocity =
2.5m/s NW, etc.
Why does direction
matter?
Consider the following question:
• Shelby runs 2 miles North and
then 4 miles South. Determine the
distance she traveled and her
final displacement.
Shelby’s Distance
• To calculate distance, we add
up the numbers that she has
traveled (ignoring the direction
b/c distance is a scalar).
• 2 miles + 4 miles =
• 6 miles
Shelby’s Displacement
• The first step in solving for any
vector is to draw a vector diagram.
• A vector diagram is a simple drawing
that represents the magnitude and
directions of the vectors in the
problem.
• All vectors are drawn as a single
headed arrow with proportionate
lengths and labels.
Shelby’s Displacement
Which is the BEST vector diagram to
represent her displacement?
4mi S
2mi N
4mi S
2mi N
origin
origin
2mi N
4mi S
origin
Shelby’s Displacement
The 3 Rules of Adding Vectors
1. Vectors in the same direction can be added
together (keep the same direction)
2. Vectors in the opposite direction can be
subtracted (the direction follows the larger
number)
3. Vectors that are at right angles can be added
using the Pythagorean Theorem
Shelby’s Displacement
So, rule 1 doesn’t apply, but rule
2 is very important.
• 2mi N - 4mi S =
• 2mi S
2mi N
4mi S
origin
• The answer of vector addition
is called the resultant.
Another question
Consider the following question:
Hayden takes 3 steps forward, 2 steps to
the right, 4 steps backward, 2 steps to
the left. Determine the distance she
traveled and her final displacement.
Hayden’s Distance
• To calculate distance, we simply
add up the steps that Hayden took
and end up with a total number.
• 3+2+4+2=
• 11 steps
• (This number is always positive).
Hayden’s Displacement
To calculate the
2 right
resultant, we must
start by drawing a
diagram that
3 forward
4 backward
represents
Hayden’s
origin
movement from
the origin.
2 left
Notice that all vectors
have a length and a
direction when drawn
Hayden’s Displacement
• In Hayden’s problem, we cannot use
Rule 1… none of the directions are the
same.
2 right
3 forward
4 backward
origin
2 left
Hayden’s Displacement
• Follow Rule 2
• Forward and backward are opposites.
• 3 forward - 4 backward =
• 1 backward
• Right and left are opposites.
• 2 right - 2 left =
• 0 (no direction on zero)
• Because we are left with only 1 vector
at the end of this step, we have found
the answer (the resultant) to be 1 step
backward.
Homework
Textbook:
Page 53 #49-53, 56
Page 54 #60