motion graphs position vs. time. vocabulary position where you are relative to the origin (reference...
DESCRIPTION
Anatomy of a Position vs time graph The x-axis represents time The Y-axis represents the object’s position relative to the origin The origin represents where the observer is standing Any points above the x-axis are on the positive side of the observer (North, East, Right, above) Any points below the x-axis are on the negative side of the observer (South, West, Left, Below) The y-intercept shows the initial position of the object A line on the graph represents the motion for that period of time Any point on the graph represents the position of the object at that moment in time A horizontal line represents the object STANDING STILL A diagonal with a negative slope represents moving at a constant velocity in the negative direction A horizontal line represents the object STANDING STILL A diagonal with a positive slope represents moving at a constant velocity in the positive directionTRANSCRIPT
Motion GraphsPosition 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 x-axis represents time
The Y-axis represents the object’s position relative to the origin
The origin represents where the observer is standing
Any points above the x-axis are on the positive side of the observer (North, East, Right, above)
Any points below the x-axis are on the negative side of the observer (South, West, Left, Below)
The y-intercept shows the initial position of the object
The y-intercept shows the initial position of the object
A line on the graph represents the motion for that period of time
Any point on the graph represents the position of the object at that moment in time
A horizontal line represents the object STANDING STILL
A diagonal with a negative slope represents moving at a constant velocity in the negative direction
A horizontal line represents the object STANDING STILL
A diagonal with a positive slope represents moving at a constant velocity in the positive direction
Anatomy of a Position vs time graph
Steep lines (high slope) mean the objects are moving fast
Shallow lines (low slope) mean the objects are moving slow
Lines that crisscross mean the objects pass each other
Position (m)
Time (s)
Anatomy of a Position vs time graph
A curve with an increasing slope means accelerating (this one is in the negative direction)
A curve with an increasing slope means accelerating (this one is in the positive direction)
A curve with a decreasing slope means slowing down (this one is in the negative direction)
A curve with a decreasing slope means slowing down (this one is in the positive direction)
Position (m)
Time (s)
Anatomy of a Position vs time graphThe slope of the line IS the velocity of the object!
Position (m)
Time (s)2
8
3
Time (s)Positi
on (m
)
Standing still on the right Standing still on the left
Starting on the left and accelerating to the right Starting on the right and decelerating to the left
Starting on the left moving quickly to the right then slowing down A car moving at a constant positive speed, slowing down to a stop then speeding back up to the same constant speed
Time (s)Positi
on (m
)
Time (s)Positi
on (m
)
Time (s)Positi
on (m
)
Time (s)Positi
on (m
)
Time (s)Positi
on (m
)
Time (s)
Positi
on
(m)
Time (s)
Positi
on (m
)
Time (s)
Positi
on
(m) Time (s)
Positi
on (m
)Time (s)
Positi
on
(m) Time (s)
Positi
on (m
)
Starting on the left and moving to the right at constant velocity Starting on the right and moving to the right at constant velocity
Standing still on the left for 4 seconds then accelerating to the right Starting on the left an moving at a constant speed to the right for 2 seconds then stopping at the observer
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
Starting at the origin and accelerating to the left then reaching a constant speed
Based on the Position vs. Time graph below, answer the following questions1. Where is the object when
time starts?2. Where is the object when
time ends?3. What is the object’s
displacement?4. During which time
period(s) is the object at rest?
5. During which time period(s) is the object speeding up?
Positi
on (m
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9
Based on the Position vs. Time graph below, answer the following questions6. During which time
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?
Positi
on (m
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9
Based on the Position vs. Time graph below, answer the following questions1. Where is the object when
time starts?2. Where is the object when
time ends?3. What is the object’s
displacement?4. What distance did the
object travel?5. During which time
period(s) is the object at rest?
Positi
on (m
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10
Based on the Position vs. Time graph below, answer the following questions6. During which time period 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
- 2 seconds- 4 seconds- 8 seconds
9. When does the object turn around?
10. When is the object moving the fastest?
Positi
on (m
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10
Position vs. Time Graphsy-intercept
slope above x-axis below x-axis
flat line positive slope negative slope
steep line shallow line
increasing slope decreasing slope graphs crossing
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
Based on the Position vs. Time graph below, answer the following questions1. How far apart do the
objects start?2. When do they cross paths?3. Which one is moving faster?4. What is the average speed
of the red car?5. How far apart are they after
10 seconds?6. Which one traveled farther?7. Do they ever have the same
speed?
Positi
on (m
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10
Anatomy of a Velocity vs Time graph
The x-axis represents time
The Y-axis represents the object’s VELOCITY
The origin represents a velocity of zero
Any points above the x-axis mean the object is MOVINGin the positive direction. (North, East, Right, above)
Any points below the x-axis mean the object is MOVINGin the negative direction (South, West, Left, Below)
The y-intercept shows the initial VELOCITY of the object
The y-intercept shows the initial VELOCITY of the object
Any point on the graph represents the VELOCITY of the object at that moment in time
A horizontal line ON THE X-AXIS represents the object STANDING STILL
A diagonal line moving AWAY from the x-axis means accelerating (speeding up)
A horizontal line represents the object moving at a CONSTANT velocity
A diagonal moving TOWARDS the x-axis means slowing down.
Crossing the a-axis means stopping and turning around and speeding back up in the other direction
Anatomy of a Velocity vs time graph
The Y-axis represents the object’s VELOCITY
The SLOPE of the line is the acceleration of the object
= (5m/s)/ 10s= 0.5m/s2
The AREA between the line and the x-axis is the DISPLACEMENT of the object
= (1/2) 10s x 5m/s=25m
5m/s
10s
Time (s)Velo
city
(m/s
)
Standing still on the right Standing still on the left
Starting at rest and accelerating to the right Starting at 20m/s to the right and decelerating
moving quickly to the right then slowing down A car moving at a constant positive speed, slowing down to a stop then speeding back up to the same constant speed
Time (s)Velo
city
(m/s
)
Time (s)Velo
city
(m/s
)
Time (s)Velo
city
(m/s
)
Time (s)Velo
city
(m/s
)
Time (s)Velo
city
(m/s
)
Time (s)
Velo
city
(m/s
)
Time (s)
Velo
city
(m/s
)
Time (s)
Velo
city
(m/s
)
Time (s)
Velo
city
(m/s
)
Time (s)
Velo
city
(m/s
)
Time (s)
Velo
city
(m/s
)
moving to the right at constant velocity Moving to the left at a constant velocity
Standing still for 4 seconds then accelerating to the right Moving at a constant speed to the right for 2 seconds then stopping slowly
moving to the left at a constant velocity, stopping, then turning around and returning to the original position at the same constant speed
accelerating to the left then reaching a constant speed
Based on the Velocity vs. Time graph below, answer the following questions1. How fast and in what
direction is the object moving when time starts?
2. How fast and in what direction is the object moving when time ends?
3. How far does the object travel in the first 2 seconds?
4. What total distance did the object travel in 7seconds?
5. What is the average speed of the object?
Velo
city
(m/s
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10
Based on the Velocity vs. Time graph below, answer the following questions6. When is the object slowing
down?7. What it the acceleration
during a. the first 2 secondsb. 2-5 secondsc. 5-7 seconds
8. Does the object turn around?Ve
loci
ty (m
/s)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10
Based on the Velocity vs. Time graph below, answer the following questions1. How fast and in what
direction is the object moving when time starts?
2. How fast and in what direction is the object moving when time ends?
3. How far does the object travel in the first 3 seconds?
4. What total distance did the object travel in 10 seconds?
5. What is the total displacement of the object after 10 seconds?
Velo
city
(m/s
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10
Based on the Velocity vs. Time graph below, answer the following questions6. During what interval is the
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?
Velo
city
(m/s
)
Time (s)
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 7 8 9 10