Position-Time and Velocity-Time Graphs：位置的时间和速度时间曲线图
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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?
Speeding up in negative direction.
Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
pos. (m)
time (s)
pos. (m)
time (s)
Position-Time Graphs
Show an object’s position as a function of time.
x-axis: time y-axis: position
Position-Time Graphs
Imagine a ball rolling along a table, illuminated by a strobe light every second.
change in y
50
slope =
change in x
(30 m – 10 m)
position (m)
40 30 20 10
slope =
(30 s – 0 s) (20 m)
slope =
10 20 30 40
(30 s)
time (s)
slope = 0.67 m/s
Position-Time Graphs
Constant speed in negative direction.
Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
pos. (m)
time (s)
A horizontal segment means the object is at rest.
0s 1s 2s
3s 4s 5s 6s 7s 8s
9 s 10 s
You can plot the ball’s position as a function of time.
Position-Time Graphs
10
9
8 position (cm) 7
6
5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9 10
Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
pos. (m)
time (s)
pos. (m)
time (s)
Constant speed in positive direction.
Traveling in positive direction, but slowing down.
Traveling in negative direction, but slowing down.
Position-Time Graphs
The slope of a P-T graph is equal to the object’s velocity in that segment.
What kind of motion created this graph?
10
Constant speed
Position-Time Graphs
Each type of motion has a characteristic shape on a P-T graph.
Constant speed Zero speed (at rest) Accelerating (speeding up) Decelerating (slowing down)
Acceleration = change in velocity over time. Not necessarily speeding up! Not necessarily slowing down!
Positive slope = positive acceleration.
Negative slope = negative acceleration.
Position-Time Graphs
position (cm)
What are the characteristics of this graph?
10 9 8 7
6
5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9
Straight line, upward slope
Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
pos. (m)
time (s)
pos. (m)
time (s)
Speeding up in positive direction.
The following P-T graph corresponds to an object moving back and forth along a straight path. Hale Waihona Puke Baiduan you describe its movement based on the graph?
N
position (m)
time (s)
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.
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?
Speeding up in negative direction.
Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
pos. (m)
time (s)
pos. (m)
time (s)
Position-Time Graphs
Show an object’s position as a function of time.
x-axis: time y-axis: position
Position-Time Graphs
Imagine a ball rolling along a table, illuminated by a strobe light every second.
change in y
50
slope =
change in x
(30 m – 10 m)
position (m)
40 30 20 10
slope =
(30 s – 0 s) (20 m)
slope =
10 20 30 40
(30 s)
time (s)
slope = 0.67 m/s
Position-Time Graphs
Constant speed in negative direction.
Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
pos. (m)
time (s)
A horizontal segment means the object is at rest.
0s 1s 2s
3s 4s 5s 6s 7s 8s
9 s 10 s
You can plot the ball’s position as a function of time.
Position-Time Graphs
10
9
8 position (cm) 7
6
5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9 10
Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
pos. (m)
time (s)
pos. (m)
time (s)
Constant speed in positive direction.
Traveling in positive direction, but slowing down.
Traveling in negative direction, but slowing down.
Position-Time Graphs
The slope of a P-T graph is equal to the object’s velocity in that segment.
What kind of motion created this graph?
10
Constant speed
Position-Time Graphs
Each type of motion has a characteristic shape on a P-T graph.
Constant speed Zero speed (at rest) Accelerating (speeding up) Decelerating (slowing down)
Acceleration = change in velocity over time. Not necessarily speeding up! Not necessarily slowing down!
Positive slope = positive acceleration.
Negative slope = negative acceleration.
Position-Time Graphs
position (cm)
What are the characteristics of this graph?
10 9 8 7
6
5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9
Straight line, upward slope
Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
pos. (m)
time (s)
pos. (m)
time (s)
Speeding up in positive direction.
The following P-T graph corresponds to an object moving back and forth along a straight path. Hale Waihona Puke Baiduan you describe its movement based on the graph?
N
position (m)
time (s)
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.