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
Slope = average velocity

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 velocity 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.
Zero speed (at rest)
Constant velocity
Accelerating

8. Position-Time Graphs
Constant velocity is represented by a straight segment on the P-T graph.
time (s)
pos. (m)
Constant velocity in positive direction.
time (s)
pos. (m)
Constant velocity in negative direction.

9. 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.

10. Position-Time Graphs
Curved segments on the P-T graph mean the object’s velocity is changing.
time (s)
pos. (m)
Increasing velocity in positive direction.
time (s)
pos. (m)
Increasing velocity in negative direction.

11. 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

12. 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

13. 5.2 Velocity vs. Time X-axis is the “time” Y-axis is the “velocity”
Slope of the line = average acceleration

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.
Negative slope = negative acceleration.
Not necessarily slowing down!

15. Velocity-Time Graphs
A horizontal line on the V-T graph means constant velocity so no acceleration.
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 vs. Time Horizontal lines = constant velocity
Sloped line = changing velocity
Steeper = greater change in velocity per second

19. Velocity-Time Graphs
If the V-T line has a positive slope, the object is undergoing acceleration in positive direction.

20. Velocity-Time Graphs V-T graph has positive slope. N S
time (s)
velocity (m/s) N S
Positive velocity and constant positive acceleration

21. 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

22. Velocity-Time Graphs
If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction.

23. 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)