position-time and velocity-time graphs
DESCRIPTION
Position-Time and Velocity-Time Graphs. Questions for Consideration. What is a position-time graph? What is a velocity-time graph? How do features on one graph translate into features on the other?. Position-Time Graphs. Show an object’s position as a function of time. x-axis: time - PowerPoint PPT PresentationTRANSCRIPT
Position-Time and Velocity-Time Graphs
Questions for Consideration
What is a position-time graph?What is a velocity-time graph?How do features on one graph translate
into features on the other?
Position-Time Graphs
Show an object’s position as a function of time. x-axis: time y-axis: position Slope = average velocity
Position-Time Graphs
Imagine a ball rolling along a table, illuminated by a strobe light every second.
You can plot the ball’s position as a function of time.
0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s
Position-Time Graphs
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1
2
3
4
5
6
7
8
9
10
time (s)
posi
tion
(cm
)
Position-Time Graphs
What are the characteristics of this graph?Straight line, upward
slopeWhat kind of motion
created this graph?Constant velocity
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
time (s)
posi
tion
(cm
)
Position-Time Graphs
Each type of motion has a characteristic shape on a P-T graph.Zero speed (at rest)Constant velocityAccelerating
Position-Time Graphs
Constant velocity is represented by a straight segment on the P-T graph.
time (s)
pos.
(m
)
Constant speed in positive direction.
time (s)
pos.
(m
)
Constant speed in negative direction.
Position-Time Graphs
An object not moving is represented by a straight segment on the P-T graph.
time (s)
pos.
(m
)
A horizontal segment means the object is at rest.
Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
time (s)
pos.
(m
)
Speeding up in positive direction.
time (s)
pos.
(m
)
Speeding up in negative direction.
Position-Time Graphs
The slope of a P-T graph is equal to the object’s velocity in that segment.
time (s)
posi
tion
(m)
10 20 30 40
10
20
30
40
50slope =
change in y
change in x
slope = (30 m – 10 m)
(30 s – 0 s)
slope = (20 m)
(30 s)
slope = 0.67 m/s
Position-Time Graphs
The following P-T graph corresponds to an object moving back and forth along a straight path. Can you describe its movement based on the graph?
time (s)
posi
tion
(m)
N
S
Answer the questions about the graph.
5.2 Velocity vs. Time
X-axis is the “time”
Y-axis is the “velocity”
Slope of the line = average acceleration
Velocity vs. Time
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5 6 7 8 9 10
Time (s)
Vel
coit
y (m
/s)
Velocity-Time Graphs
A velocity-time (V-T) graph shows an object’s velocity as a function of time.A horizontal line = constant velocity.A straight sloped line = constant
acceleration.Acceleration = change in velocity over time.
Positive slope = positive acceleration.Negative slope = negative acceleration.
Not necessarily slowing down!
Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity.
time (s)
velo
city
(m
/s)
N
S
Object is moving at a constant velocity North.
Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity.
time (s)
velo
city
(m
/s)
N
S
Object is moving at a constant velocity South.
Velocity-Time Graphs
If an object isn’t moving, its velocity is zero.
time (s)
velo
city
(m
/s)
N
S
Object is at rest
Velocity vs. Time
Horizontal lines = constant velocitySloped line = changing velocity
Steeper = greater change in velocity per second
Velocity-Time Graphs
If the V-T line has a positive slope, the object is undergoing acceleration in positive direction.
Velocity-Time Graphs
V-T graph has positive slope.
time (s)
velo
city
(m
/s)
N
S Positive velocity and constant positive acceleration
Slope of V vs. T graph
Slope = rise/run
Pick two points on the line: (0,0) (2,2)
Slope = (2-0)/(2-0) = 1.0 m/s2
Slope = Average acceleration of the object
Velocity-Time Graphs
If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction.
Velocity-Time Graphs
V-T graph has negative slope.
time (s)
velo
city
(m
/s)
N
S Positive velocity and negative acceleration: object is slowing down,
time (s)
velo
city
(m
/s)
N
SNegative velocity and negative acceleration: object is speeding up! (in negative direction)