Motion
graphs
pg.11
Objectives
•
•
•
Physics terms
Create and interpret graphs of
position versus time.
•
slope
•
average velocity
Calculate velocity from the
slope of the position vs. time
graph.
•
instantaneous velocity
Create and interpret graphs of
velocity versus time.
Equations
Graphing motion
In order to understand motion, you first need be able
to describe it.
One way to do this is with graphs.
The simplest motion graph shows the position of an
object at each moment of time.
Position vs. time
Position vs. time graphs show how the position of an
object changes over time.
• Position (+/-) is on the vertical (y) axis
• Time is on the horizontal (x) axis
Each point on the graph
represents an object being at a
particular place at a particular
time.
Position vs. time graph practice
How would you represent
an object at a position of
10 meters at 8 seconds?
How would you represent an
object at a position of -2m at
2 seconds?
Creating a position vs. time graph
• Follow the steps given below to draw the correct
position vs. time graph using the graph on the next
slide:
• You start at 0 meters at t = 0 seconds
• Then you move to a position of 12 meters at 4 seconds
• Now you’re tired so you stop for one second
• Next you move back to 0m in the next 4 seconds.
Creating a position vs. time graph
P vs. t graph & velocity
• For line 1 on your graph (from 0s-4s):
–
–
–
–
–
Object is: Changing position
OR
Staying still
Position change is: Constant
OR
Not constant
OR Zero
Speed is:
Constant
OR
Not constant
Velocity is: Positive
OR
Negative OR
Zero
Slope is:
Positive
OR
Negative OR
Zero
• For line 2 on your graph (from 4s-5s):
–
–
–
–
–
Object is: Changing position
OR
Staying still
Position change is: Constant
OR
Not constant
OR Zero
Speed is:
Constant
OR
Not constant
Velocity is: Positive
OR
Negative OR
Zero
Slope is:
Positive
OR
Negative OR
Zero
P vs. t graph & velocity
• For line 3 on your graph (from 5s-9s):
–
–
–
–
–
Object is: Changing position
OR
Staying still
Position change is: Constant
OR
Not constant
OR Zero
Speed is:
Constant
OR
Not constant
Velocity is: Positive
OR
Negative OR
Zero
Slope is:
Positive
OR
Negative OR
Zero
Velocity vs. time
Velocity vs. time graphs show how an object’s
velocity changes over time.
• Velocity (+/-) is on the
vertical (y) axis
• Time is on the
horizontal (x) axis
Velocity vs. time graph practice
• How would you represent an
object moving with a constant
velocity of 4m/s for 8
seconds?
• How would you represent an
object moving with a constant
velocity of -2m/s for 4s & then
changing its speed by 2m/s
every second for 4s?
Creating a velocity vs. time graph
• Follow the steps given below to draw the correct
velocity vs. time graph using the graph on the next
slide:
• An object moves forward at 5m/s for 5 seconds
• Then it turns around & moves backward at 5m/s for 5
more seconds
Creating a velocity vs. time graph
Importance of Slope
Finding slope can help us describe how an object’s
motion is changing.
Taking the slope of a line on a position vs. time
graph tells you the objects velocity.
Taking the slope of a line on a velocity vs. time
graph tells you the objects acceleration.
Slope
To find slope of a line pick 2
points on the line & plug them
into the slope formula
Using slope
• Below on the left is a p vs. t graph. Draw the V vs. t
graph that corresponds to the p vs. t graph.
Put the graphs together
An object moves from 0 meters to
12 meters in 4 seconds.
Next, it stands still for 1 second,
then moves back again in 4 more
seconds.
3 m/s
Put the graphs together
An object moves from 0 meters to
12 meters in 4 seconds.
Next, it stands still for 1 second,
then moves back again in 4 more
seconds.
What does the velocity graph look like?
3 m/s
Put the graphs together
An object moves from 0 meters to
12 meters in 4 seconds.
Next, it stands still for 1 second,
then moves back again in 4 more
seconds.
3 m/s
-3 m/s
Instantaneous velocity
In most situations the velocity is
not constant.
The instantaneous velocity is the
velocity at a given instant.
Can you find this object’s
instantaneous velocity at:
•
4 seconds?
•
8 seconds?
•
13 seconds?
Average velocity
End at 70 m
The average velocity is
the total change in
position divided by the
total change in time.
Start at 15 m
𝑉𝑎𝑣𝑔
𝑥𝑓 − 𝑥𝑖
∆𝑥
=
=
∆𝑡
𝑡𝑓 − 𝑡𝑖
What is the object’s
average velocity?
Start at 3 s
End at 14 s
Homework
1. Where is the speed zero?
At (B), where the slope is zero.
2. Where do the two graphs NOT
match?
At (C); the position graph has a slope of 2
m/s, but the velocity graph shows 4 m/s.
3. Where is the motion forward and
where is it backward?
(A) and (C) are forward, (D) is backward.
4. Between 1 and 2 seconds, how much
distance is covered?
6 meters
Homework
4. Sketch these graphs if the
velocity at (A) and (C) were
changed to 3 m/s.