1. Position-Time and Velocity-Time Graphs

2. 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?

3. Position-Time Graphs Show an object’s position as a function of time.
x-axis: time
y-axis: position

4. Position-Time Graphs 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s
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

5. Position-Time Graphs 1 2 3 4 5 6 7 8 9 10
position (cm)
time (s)

6. Position-Time Graphs What are the characteristics of this graph?
Straight line, upward slope
What kind of motion created this graph?
Constant speed 1 2 3 4 5 6 7 8 9 10
time (s)
position (cm)

7. 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)

8. Position-Time Graphs
Constant speed 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.

9. Position-Time Graphs
Constant speed is represented by a straight segment on the P-T graph.
time (s)
pos. (m)
A horizontal segment means the object is at rest.

10. 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.

11. Position-Time Graphs
Curved segments on the P-T graph mean the object’s speed is changing.
time (s)
pos. (m)
Traveling in positive direction, but slowing down.
time (s)
pos. (m)
Traveling in negative direction, but slowing down.

12. Position-Time Graphs
The slope of a P-T graph is equal to the object’s velocity in that segment.
slope =
change in y
change in x
time (s)
position (m) 10 20 30 40 50
slope =
(30 m – 10 m)
(30 s – 0 s)
slope =
(20 m)
(30 s)
slope = 0.67 m/s

13. 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)
position (m) N S

14. 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.
Not necessarily speeding up!
Negative slope = negative acceleration.
Not necessarily slowing down!

15. Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity.
time (s)
velocity (m/s) N S
Object is moving at a constant velocity North.

16. Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity.
time (s)
velocity (m/s) N S
Object is moving at a constant velocity South.

17. Velocity-Time Graphs If an object isn’t moving, its velocity is zero.
time (s)
velocity (m/s) N S
Object is at rest

18. Velocity-Time Graphs
If the V-T line has a positive slope, the object is undergoing acceleration in positive direction.
If v is positive also, object is speeding up.
If v is negative, object is slowing down.

19. Velocity-Time Graphs V-T graph has positive slope. N S
time (s)
velocity (m/s) N S
Positive velocity and positive acceleration: object is speeding up!
time (s)
velocity (m/s) N S
Negative velocity and positive acceleration: object is slowing down.

20. Velocity-Time Graphs
If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction.
If v is positive, the object is slowing down.
If v is negative also, the object is speeding up.

21. Velocity-Time Graphs V-T graph has negative slope. N S
time (s)
velocity (m/s) N S
Positive velocity and negative acceleration: object is slowing down,
time (s)
velocity (m/s) N S
Negative velocity and negative acceleration: object is speeding up! (in negative direction)