1. Graphing Motion Position vs. Time Stationary objects
Position is same at every time (d = 0)
So speed = 0
Stationary objects

2. Graphing Motion Objects with constant speed
Position t
Position changes same amount every interval
If it moves 2m in 1st second, it will move 2m every second
Objects with constant speed

3. Graphing Motion Objects with constant velocity
Position 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
Objects with constant velocity
Change in position
Change in time

4. Interpreting Graphs What’s going on here?
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)
What’s going on here?
Position t

5. Graphing Speed vs. Time
For constant speed (could be sitting still, could be moving), speed doesn’t change
Graph is just a flat line
REMEMBER: This is just the slope of the position/time graph!
Position
Speed
Case 2: Positive Constant Speed
Case 2: Positive Constant Velocity
Case 1: No Motion
Case 1: No Motion t t

6. Area under the curve
Question: What does the area under the Velocity vs. Time graph tell you? 4 3 2 1
Speed (m/s)
Time (s)
Answer: velocity x time = distance

7. Area under the curve It works for changing velocity, too!4 3 2 1
Speed (m/s)
Time (s)
What is the total displacement?
Area of the triangle: ½ * 4 * 4 = 8 meters

8. What’s happening here? We call it Acceleration
Getting faster and faster
Slope increases, therefore…
Speed increases
We call it Acceleration
Speed t
Position t

9. 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)

10. Acceleration Notes
Uniform (or constant) acceleration: when an object accelerates at a constant rate over a period of time.
Acceleration = change in velocity/time interval
Speed t

11. Acceleration Notes
Mathematically: a = Δv = “change in velocity” v = final velocity vo = initial velocity
Units: (m/s) or m s s2
Δv = v -vo t t

12. 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/s t 3s
The car accelerates at 3 m/s2.

13. Finding Acceleration on a Velocity Graph
For linear change in velocity, acceleration is the slope of the velocity graph
Positive slope, so positive acceleration
Speed
Slope = accel = 0
Negative slope, so neg. acceleration (sometimes called “deceleration” t

14. Average Speed
If the speed is changing linearly (constant acceleration)
Average speed is just the average of the initial and final speeds
vave = v + vo t V
Vave Vo

15. Average Speed: Careful!
If I accelerate uniformly from 10 to 20 mph (miles per hour), what’s my average speed?
Constant acceleration: ½ * ( ) = 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!!!