Motion Graphs
Position vs. time
Vocabulary
• Position
• Where you are relative to the origin (reference point/observer)
• Distance
• The total length of how far you move in a give time period
• Displacement
• Overall change in position (final position – initial position)
• Average speed
• Total distance / total time
• Average velocity
• Displacement / time
• Instantaneous speed (or velocity)
• The speed or velocity at one moment in time
• Positive acceleration
• Increasing your velocity
• Negative acceleration
• Decreasing your velocity
Anatomy of a Position vs time graph
The y-intercept shows
the initial position of
the object
The
represents
Theorigin
y-intercept
shows
where
the position
observerofis
the initial
standing
the object
A horizontal line
represents the object
STANDING STILL
A diagonal with a positive
Any points above the x-axis are on the positive side of
slope represents moving
the observer (North, East, Right, above)
at a constant velocity in
A diagonal with a negative
the positive direction
slope represents moving
at a constant velocity in
the negative direction
Any point on the graph
position
thenegative side of
Any pointsrepresents
below thethe
x-axis
are onofthe
at Athat
moment
inLeft,
timeBelow)
theobject
observer
(South,
West,
horizontal
line
represents the object
A line on the graph STANDING STILL
The Y-axis represents
the object’s position
relative to the origin
represents the motion for
that period of time
The x-axis represents
time
Anatomy of a Position vs time graph
Position (m)
Steep lines (high slope)
mean the objects are
moving fast
Shallow lines (low slope)
mean the objects are
moving slow
Time (s)
Lines that crisscross mean
the objects pass each
other
Anatomy of a Position vs time graph
Position (m)
A curve with a decreasing
slope means slowing
Adown
curve(this
withone
an increasing
is in the
slope
means
accelerating
negative direction)
(this one is in the positive
direction)
Time (s)
A curve with an increasing
slope means accelerating
(this one is in the negative
direction)
A curve with a decreasing
slope means slowing
down (this one is in the
positive direction)
Anatomy of a Position vs time graph
Position (m)
The slope of the line IS
the velocity of the object!
∆𝑦
𝑠𝑙𝑜𝑝𝑒 =
∆𝑥
8
8−2 𝑚
=
3−0 𝑠
2𝑚/𝑠
2
3
Time (s)
Standing still on the left
Position (m)
Position (m)
Standing still on the right
Time (s)
Starting on the right and decelerating to the left
Position (m)
Position (m)
Starting on the left and accelerating to the right
Time (s)
Time (s)
Time (s)
A car moving at a constant positive speed, slowing down to a stop then speeding
back up to the same constant speed
Position (m)
Starting on the left moving quickly to the right then slowing down
Position (m)
Time (s)
Time (s)
Position
(m)
Standing still on the left for 4 seconds then accelerating to the right
Time (s)
Position
(m)
Starting on the right and moving to the left at a constant velocity, stopping, then
turning back around and returning to the original position at the same constant
speed
Time (s)
Position (m)
Time (s)
Starting on the left an moving at a constant speed to the right for 2 seconds then
stopping at the observer
Position (m)
Time (s)
Starting on the right and moving to the right at constant velocity
Time (s)
Starting at the origin and accelerating to the left then reaching a constant speed
Position (m)
Position
(m)
Starting on the left and moving to the right at constant velocity
Time (s)
Based on the Position vs. Time graph below, answer the
following questions
1. Where is the object when
6
2.
5
4
3.
3
Position (m)
2
1
4.
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
Time (s)
5.
time starts?
Where is the object when
time ends?
What is the object’s
displacement?
During which time
period(s) is the object at
rest?
During which time
period(s) is the object
speeding up?
Based on the Position vs. Time graph below, answer the
following questions
6. During which time
6
5
4
3
Position (m)
2
1
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
Time (s)
period(s) is the object
slowing down?
7. During which time
period(s) is the object
moving at a constant
velocity?
8. How fast is the object
moving at 6 seconds?
9. What is the object’s overall
average speed?
Based on the Position vs. Time graph below, answer the
following questions
1. Where is the object when
6
2.
5
4
3.
3
Position (m)
2
1
4.
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
10
Time (s)
5.
time starts?
Where is the object when
time ends?
What is the object’s
displacement?
What distance did the
object travel?
During which time
period(s) is the object at
rest?
Based on the Position vs. Time graph below, answer the
6. During which time period
following questions
is the object moving to the
right?
7. During which time period
is the object moving to the
left?
8. What is the velocity of the
object at
6
5
4
3
Position (m)
2
1
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
10
Time (s)
- 2 seconds
- 4 seconds
- 8 seconds
9. When does the object turn
around?
10. When is the object moving
the fastest?
Do Now: Copy this in
your notes and fill out
what each piece of a
position vs. time graph
tells you about the
object and its position
or motion.
HW:
Complete position vs.
time worksheet
Position vs. Time Graphs
y-intercept
slope
above x-axis
below x-axis
flat line
positive slope
negative slope
steep line
shallow line
increasing slope
decreasing slope
graphs crossing
Based on the Position vs. Time graph below, answer the
following questions
1. How far apart do the
6
2.
3.
4.
5
4
3
Position (m)
2
1
5.
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
10
Time (s)
6.
7.
objects start?
When do they cross paths?
Which one is moving faster?
What is the average speed
of the red car?
How far apart are they after
10 seconds?
Which one traveled farther?
Do they ever have the same
speed?
Anatomy of a Velocity vs Time graph
The y-intercept shows
the initial VELOCITY of
the object
The
represents
Theorigin
y-intercept
shows
athe
velocity
of
zero
initial VELOCITY of
the object
Any point on the graph
represents the VELOCITY of the
Crossing the a-axis means
object at that moment in time
stopping and turning
Any points above the x-axis mean the object is MOVING
around and speeding back
in the positive direction. (North, East, Right, above)
up in the other direction
A horizontal line ON THE
X-AXIS represents the
object STANDING STILL
The x-axis represents
A diagonal moving time
A diagonal line moving
TOWARDS
the x-axis
AWAY from the x-axis Any points below the x-axis mean the object
is MOVING
means
slowing down.
means accelerating
in the negative
direction
Below)
A horizontal
line (South, West, Left,
(speeding up)
represents the object
moving at a CONSTANT
velocity
The Y-axis represents
the object’s VELOCITY
Anatomy of a Velocity vs time graph
5m/s
The Y-axis represents
the object’s VELOCITY
The AREA between the line and
the x-axis is the DISPLACEMENT
of the object
𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐴𝑟𝑒𝑎 = 1 2 𝑏ℎ
= (1/2) 10s x 5m/s
=25m
10s
The SLOPE of the line is
the acceleration of the
object
∆𝑦
𝑠𝑙𝑜𝑝𝑒 =
∆𝑥
= (5m/s)/ 10s
= 0.5m/s2
Standing still on the left
Velocity (m/s)
Velocity (m/s)
Standing still on the right
Time (s)
Starting at 20m/s to the right and decelerating
Velocity (m/s)
Velocity (m/s)
Starting at rest and accelerating to the right
Time (s)
Time (s)
A car moving at a constant positive speed, slowing down to a stop then speeding
back up to the same constant speed
Velocity (m/s)
moving quickly to the right then slowing down
Velocity (m/s)
Time (s)
Time (s)
Time (s)
Time (s)
Velocity (m/s)
moving to the left at a constant velocity, stopping, then turning around and
returning to the original position at the same constant speed
Time (s)
Time (s)
Moving at a constant speed to the right for 2 seconds then stopping slowly
Velocity (m/s)
Velocity (m/s)
Standing still for 4 seconds then accelerating to the right
Time (s)
accelerating to the left then reaching a constant speed
Velocity (m/s)
Velocity (m/s)
Time (s)
Velocity (m/s)
Moving to the left at a constant velocity
moving to the right at constant velocity
Time (s)
Based on the Velocity vs. Time graph below, answer the
following questions
1. How fast and in what
6
5
2.
4
Velocity (m/s)
3
2
3.
1
0
-1
-2
1
2
3
4
5
6
7
8
9
10
Time (s)
4.
-3
-4
-5
-6
5.
direction is the object
moving when time starts?
How fast and in what
direction is the object
moving when time ends?
How far does the object
travel in the first 2
seconds?
What total distance did the
object travel in 7seconds?
What is the average speed
of the object?
Based on the Velocity vs. Time graph below, answer the
following questions
6. When is the object slowing
down?
7. What it the acceleration
during
6
5
4
a. the first 2 seconds
b. 2-5 seconds
c. 5-7 seconds
Velocity (m/s)
3
2
1
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
10
Time (s)
8. Does the object turn
around?
Based on the Velocity vs. Time graph below, answer the
1. How fast and in what
following questions
6
5
2.
4
Velocity (m/s)
3
2
3.
1
0
-1
-2
1
2
3
4
5
6
7
8
9
10
Time (s)
4.
-3
-4
-5
-6
5.
direction is the object
moving when time starts?
How fast and in what
direction is the object
moving when time ends?
How far does the object
travel in the first 3
seconds?
What total distance did the
object travel in 10
seconds?
What is the total
displacement of the object
after 10 seconds?
Based on the Velocity vs. Time graph below, answer the
following questions
6. During what interval is the
6
5
4
Velocity (m/s)
3
2
1
0
-1
-2
-3
-4
-5
-6
1
2
3
4
5
6
7
8
9
10
Time (s)
object moving left?
7. During what interval is the
object moving right?
8. When is the object
speeding up?
9. When is the object slowing
down?
10. When does the object turn
around?
11. What is the acceleration of
the object between 6 and
10 seconds?