Graphing Motion
Position vs. Time

Position is same at
every time
(d = 0)
So speed = 0

Stationary objects
Position

t


Position changes
same amount every
interval
If it moves 2m in 1st
second, it will move
2m every second
Position
Graphing Motion
Objects with constant
speed
t




The slope is the change in
position/ change in time
That’s the speed or
velocity!
KEY FINDING: Slope
of position/time graph
is the speed or velocity
Negative slope: object is
moving in the negative
direction
Position
Graphing Motion
Objects with constant
velocity
Change in
position
Change in
time
t
Interpreting Graphs
What’s going on here?
Position

• Starts in a positive position
• Moves forward with
constant speed
• Stops for a while
• Goes backward with
constant speed
• Goes forward with constant
speed to the origin (x = 0)
t
Graphing Speed vs. Time
Position

For constant speed (could be sitting still, could be
moving), speed doesn’t change
Graph is just a flat line
Case 2: Positive
Constant Speed
Case 1: No Motion
Speed

REMEMBER: This is
just the slope of the
position/time graph!
Case 2: Positive
Constant Velocity
Case 1: No Motion
t
t
Area under the curve

Question: What does the area under the
Velocity vs. Time graph tell you?
4
3
Speed (m/s)
2
1
0

1
2
3
4
5
Time (s)
Answer: velocity x time = distance
Area under the curve

It works for changing velocity, too!
4
3
Speed (m/s)
2
1
0
1
2
3
4
5
Time (s)
What is the total displacement?
 Area of the triangle: ½ * 4 * 4 = 8 meters

What’s happening here?


Speed
Position

Getting faster and faster
Slope increases, therefore…
Speed increases
t
We call it
Acceleration
t
Acceleration Notes
 Acceleration
is any change in speed
or direction.
 Acceleration
occurs when an object
speeds up, slows down (or changes
direction– we’ll see this later)

Uniform (or constant)
acceleration: when an
object accelerates at a
constant rate over a
period of time.

Acceleration = change in
velocity/time interval
Speed
Acceleration Notes
t
Acceleration Notes

Mathematically:
a = Δv = v -vo
t

Units: (m/s)
s
t
or
Δv = “change in
velocity”
v = final velocity
vo = initial velocity
m
s2
Acceleration Notes
Example:
A car starts out traveling at 10 m/s and
accelerates to 19 m/s in a time of 3
seconds. What is the acceleration of
the car?
 a = vf –vi = 19 m/s – 10 m/s = 3 m/s2
t
3s
 The car accelerates at 3 m/s2.

Finding Acceleration
on a Velocity Graph
For linear change in velocity, acceleration is
the slope of the velocity graph
Speed

Positive slope, so
positive
acceleration
Slope = accel = 0
Negative slope, so neg. acceleration (sometimes called
“deceleration”
t
Average Speed



If the speed is changing linearly (constant
acceleration)
Average speed is just the average of the initial
and final speeds
V
vave = v + vo
Vave
2
Vo
t
Average Speed: Careful!





If I accelerate uniformly from 10 to 20 mph
(miles per hour), what’s my average speed?
Constant acceleration: ½ * (10 + 20) = 15 mph
If I drive 10 mph for 10 miles and 20 mph for
10 miles, what’s my average speed?
13.3 mph!
Not constant acceleration, so not 15 mph!!!