1. Meaning of Graphs

2. Position vs. Time Graphs
Shape and slope of lines on the graph--give meaning.
For Position vs. Time, we can interpret the velocity.
constant, rightward (+) velocity - say of +10 m/s.
Result: motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph.

3. Accelerating Motion
rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating.
Result: a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph. (QUADRATIC)

4. Review Positive Velocity Changing Velocity (acceleration)
Constant Velocity Positive Velocity
Positive Velocity Changing Velocity (acceleration)

5. Importance of Slope – P vs. t
Remember slope of a line?
Slope reveals info about velocity
“As the slope goes, so goes the velocity”
Constant Velocity=Constant Slope (straight line)
Velocity changes=slope changes (curved line)
Velocity is positive = slope is positive (moving upwards and to the right)
Steeper slope, faster velocity

6. Which Has a Greater Velocity?
Slow, Rightward(+) Constant Velocity
Fast, Rightward(+) Constant Velocity

7. Negative Slope Slow, Leftward(-) Constant Velocity
Fast, Leftward(-) Constant Velocity

8. Back to Curved Slope Lines
Curved Lines = changing slope = acceleration
Starts with a small slope
Ends with a large slope
What does this say about it’s velocity in the beginning and the end?

9. Example:
If Paul walks three meters at 1 m/s, then stops and walks back at 1.5 m/s, what would the P vs. T graph look like?

10. Velocity vs. Time Graph
constant, rightward (+) velocity - say of +10 m/s
Note that a motion described as a constant, positive velocity results in a line of zero slope (a horizontal line has zero slope
Slope for V vs. T = acceleration

11. Accelerated Motion
A car that is moving rightward but speeding up or accelerating.
The slope of the line is positive, corresponding to the positive acceleration
rightward (+), changing velocity

12. Review Positive Velocity Zero Acceleration
Positive Velocity Positive Acceleration

13. Meaning of Slope V vs. t
Slope of a velocity-time graph reveals info about the acceleration.
Acceleration, zero = straight line (zero slope)
Positive acceleration, positive slope (upward line)
Negative acceleration, negative slope (downward sloping line)

14. Positive and Negative Positive direction, if it lies above zero.
Negative direction if it lies below zero.
Can be speeding up or slowing down.
If it crosses over zero on x-axis, it changes direction.

15. Example
If Paul walks three meters at 1 m/s, then stops and walks back at 1.5 m/s, what would the V vs. T graph look like?

16. Speeding up or Slowing down?
Speeding up if the magnitude (numerical value) of velocity is getting larger.
From 3 m/s to 9 m/s or from -3 m/s to -9 m/s.
The number itself is key, not the sign or direction.
Speed up: moving away from 0-velocity line
Slowing down: moving towards the 0-velocity line.