9/9 We will be working on graphs this week
Turn in your completed WS II from yesterday to the blue
sorter
Pick up Page 2 of Graphing Notes
Tests are graded. Corrections/Retakes will be available Tue
– Fri
Warm Up 3: What is difference between interpolate
and exctrapolate?
9/10 Yesterday we covered notes on Displacement
vs Time Graphs. You also turned in WS II.
Tests are graded. Corrections/Retakes will be available Tue
– Fri (I have duty this afternoon from 2:35-2:50)
Warm Up 4: Look at graph below. What is the net
displacement?
Displacement-Time Graph
500
displacement (meters)
400
300
200
100
Series1
0
-100
-200
-300
-400
-500
0
10
20
30
40
50
60
time (seconds)
70
80
90
100
The graphs…
Game
Motion Graphing
Distance, Velocity, and
Acceleration
Motion Graphing Reference
Displacement-Time Graph
500
displacement (meters)
400
300
200
100
Series1
0
-100
-200
-300
-400
-500
0
10
20
30
40
50
60
time (seconds)
70
80
90
100
Scalar quantity
•
•
•
•
a measurement
Magnitude
No direction implied
Ex. mass, volume, density, distance,
speed
Vector quantity
•
•
•
•
a measurement
Magnitude
Direction
Ex.: displacement, velocity, acceleration,
force
Distance
• the length of the actual path taken by the
object regardless of direction
• scalar quantity
• SI units include m, km
Displacement
• length (measured in a straight line) from
the reference point to the object (implies a
given direction)
• Sometimes on graph labeled as Position
• vector quantity
• SI units include m, km
Speed
• change in distance divided by change in
time (d/t )
• scalar quantity
• SI units include m/sec or cm/sec.
Velocity
• speed in a given direction
• magnitude and direction included in the
measurement
• vector quantity
• SI units include m/sec or cm/sec.
Acceleration
• change in velocity divided by change in
time (∆v/∆t)
• vector quantity
• SI units include m/sec2 or cm/sec2
To begin, consider a car moving with a constant,
rightward (+) velocity of 10 m/s
What would a Position vs Time graph of this
motion, look like?
The slope of the line on a position-time graph is
the velocity of the object.
And the slope is…
Example 1 A car moves in a straight line and its odometer
readings are plotted against time.
a. Find the speed of the car at points A and B.
B
m
s

40
= 0.5 m/s
80
Same for A and B
A
b. What is the car's average speed?

v = 0.5 m/s
c. What is its acceleration?
a = 0 m/s2
Ex 2. Let’s compare the motions shown here
Compare the velocity of the red line to the…
Green line
Black line
Blue line
Orange line
And this trip shows?
Now consider a car moving with a changing, rightward
(+) velocity that is, a car that is moving rightward and
speeding up or accelerating.
And the graph’s shape is?
Ex 3. What if the shape of the graph is a curve?
A curve shows a
changing velocity or
acceleration.
We can find the
Velocity at a particular
Instant. If we compare two points, we will
See that velocity is changing and therefore
We have acceleration.
The instantaneous velocity of an object at a certain
time is the slope of the position (displacement) versus
time graph at that time. It can be positive, negative,
or zero.
What shows the instantaneous speed in the car?
Summary of D v T &V vT
No motion, constant velocity, and acceleration on VvT graph
d vs t graph
•
•
•
•
•
•
•
Slope of line is velocity
Linear line represents a constant velocity
Horizontal line represents no motion
Curved line represents acceleration
Steeper slope represents greater velocity
Slope = Dd /Dt = velocity
Distance from detector CAN be indicated
Positive direction? Negative direction?
Resting?
Traveling at same speed?
v vs t graph
•
•
•
•
•
•
•
Slope of line is acceleration
Linear line represents uniform acceleration
Horizontal line represents constant velocity, a=o
Curved line represents changing acceleration
Steeper slope represents greater acceleration
Slope = Dv /Dt = acceleration
Distance from detector cannot be indicated, only
direction: away is positive and towards is negative
a vs t graph
• Linear line– acceleration is changing at a
constant rate
• Horizontal line– uniform acceleration(the
acceleration stays the same)
• Curved line– acceleration is changing nonuniformly
• Steeper slope-- greater change in a
• Slope = Da /Dt
Obj 15: Comparing graphs
No motion (v=0)
velocity vs. time
4
Series1
2
0
1
2
3
time
4
5
velocity
distance
6
1
0.8
0.6
0.4
0.2
0
acceleration vs. time
Series1
1
2
3
4
time
5
6
acceleration
Distance Vs. Time
1
0.8
0.6
0.4
0.2
0
Series1
1
2
3
4
time
5
6
Constant Velocity (a=0) positive
direction
Distance vs. time
20
Series1
10
0
velocity
6
4
Series1
2
0
1
2
3
4
time
5
6
1
2
3
time
4
5
acceleration
30
distance
acceleration vs. time
velocity Vs. Time
1
0.8
0.6
0.4
0.2
0
Series1
1
2
3
4
time
5
6
Constant velocity (a=0) negative
direction
distance vs. time
20
Series1
10
0
1
2
3
4
time
5
6
velocity
0
-2
1
2
3
4
5
6
Series1
-4
acceleration
30
distance
acceleration vs. time
velocity vs. time
1
0.8
0.6
0.4
0.2
0
Series1
1
-6
time
2
3
4
time
5
6
The graphs…
.
In this lab you will measure your
motion with a sonic motion detector.
The motion detector emits sound
waves and then detects them after they have
reflected off of some object (such as you or
your lab partners!). A computer then records
distance from the detector to the object as a
function of time. You will practice making and
interpreting position-time graphs.