# Notes - PT and VT Graphs

```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
Position-Time Graphs

Imagine a ball rolling along a table, illuminated by a strobe light
every second.
0s 1s 2s

3s 4s 5s 6s 7s 8s
You can plot the ball’s position as a function of time.
9 s 10 s
Position-Time Graphs
10
9
position (cm)
8
7
6
5
4
3
2
1
time (s)
1
2
3
4
5
6
7
8
9 10
Position-Time Graphs
What are the
characteristics of
this graph?


Straight line, upward
slope
What kind of motion
created this graph?

Constant speed
10
9
8
7
position (cm)

6
5
4
3
2
1
time (s)
1
2
3
4
5
6
7
8
9
10
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)

Position-Time Graphs
Constant speed is represented by a
straight segment on the P-T graph.
time (s)
Constant speed in positive
direction.
pos. (m)
pos. (m)

time (s)
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.
Position-Time Graphs
time (s)
Speeding up in positive
direction.
pos. (m)
Curved segments on the P-T graph
mean the object’s speed is changing.
pos. (m)

time (s)
Speeding up in negative
direction.
Position-Time Graphs
time (s)
Traveling in positive
direction, but slowing down.
pos. (m)
Curved segments on the P-T graph
mean the object’s speed is changing.
pos. (m)

time (s)
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.
change in y
slope =
50
position (m)

40
change in x
(30 m – 10 m)
30
slope =
(30 s – 0 s)
20
(20 m)
10
slope =
10
20
time (s)
30
(30 s)
40
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?
N
position (m)

S
time (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.



Positive slope = positive acceleration.


Acceleration = change in velocity over time.
Not necessarily speeding up!
Negative slope = negative acceleration.

Not necessarily slowing down!
Velocity-Time Graphs

A horizontal line on the V-T graph means
constant velocity.
velocity (m/s)
N
S
time (s)
Object is moving at
a constant velocity
North.
Velocity-Time Graphs

A horizontal line on the V-T graph means
constant velocity.
velocity (m/s)
N
S
time (s)
Object is moving at
a constant velocity
South.
Velocity-Time Graphs
If an object isn’t moving, its velocity is
zero.
N
velocity (m/s)

S
Object is at rest
time (s)
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.

Velocity-Time Graphs
V-T graph has positive slope.
N
velocity (m/s)
N
S
time (s)
Positive velocity and
positive acceleration: object
is speeding up!
velocity (m/s)

S
time (s)
Negative velocity and
positive acceleration: object
is slowing down.
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.

Velocity-Time Graphs
V-T graph has negative slope.
N
velocity (m/s)
N
S
time (s)
Positive velocity and
negative acceleration:
object is slowing down,
velocity (m/s)

S
time (s)
Negative velocity and
negative acceleration:
object is speeding up! (in
negative direction)
```