1. Describing Motion
The graphs Part II…

2. The velocity in interval 3?
The slope of a position vs time graph is?
The slope of part 2?
The slope of part 1?
The velocity in interval 3?
+ 2 m/s
-1m/s

3. Consider a car moving with a constant, rightward (+) velocity of +10 m/s.
What does a velocity vs time graph look like for this motion?
Zero Acceleration

4. Now consider a car moving with a rightward (+), changing velocity – that is, a car that is moving rightward and speeding up or accelerating.
And the graph?
The car is moving in the positive direction and speeding up, it is said to have a positive acceleration.

5. The slope of a velocity time graph is …
Slope = Δy = Change in velocity =
Δx Change in time
ACCELERATION
The instantaneous acceleration of an object at a certain time is the slope of the velocity versus time graph at that time. It can be positive, negative, or zero.

6. Positive and negative acceleration & velocity?
Acceleration and velocity are in opposite directions
Acceleration and velocity in same direction
Acceleration and velocity in same direction
Acceleration and velocity are in opposite directions

7. Describe the motion of the dot.
Constant positive velocity
What does the position vs time graph look like?
What does the velocity vs time graph look like?
What does the acceleration vs time graph look like?

8. Describe the motion of the dot.
A negative constant velocity
What does the position vs time graph look like?
What does the velocity vs time graph look like?
What does the acceleration vs time graph look like?

9. Describe the motion of the dot.
A positive velocity and a positive acceleration
What does the position vs time graph look like?
What does the velocity vs time graph look like?
What does the acceleration vs time graph look like?

10. Describe the motion of the dot.
A positive velocity and negative acceleration
What does the position vs time graph look like?
What does the velocity vs time graph look like?
What does the acceleration vs time graph look like?

11. Describe the motion of the dot.
A negative velocity and negative acceleration
What does the position vs time graph look like?
What does the velocity vs time graph look like?
What does the acceleration vs time graph look like?

12. Summary
Velocity in Quad 1: positive
Velocity in Quad 4: negative
Acceleration: positive if slope positive
negative if slope negative

13. Example: The velocity-time graph for a two-stage rocket is shown below
Example: The velocity-time graph for a two-stage rocket is shown below. Use the graph and your understanding of slope calculations to determine the acceleration of the rocket during the listed time intervals
1 to 4 sec
4 to 9 sec
9 to 12 sec
0 to 1 sec
+ 40m/s2
accelerating upward
+20 m/s2
Still accelerating upward
-20 m/s2
Decelerating & moving upward
-20 m/s2
Accelerating downward

14. 3,2,1,Blast off…

15. Area and Graphs

16. The distance covered is the “area under” the line.
Example 2:
a) What is the acceleration in interval A?
Acc = Δy = (20 – 0 m/s) =
Δx (10 – 0 s)
+ 2 m/s2
b) What distance does it travel in first the 20s?
The distance covered is the “area under” the line.
Area = ½ bh
Distance = ½ (20s)(40m/s)
Distance = 400 m

17. e) What is the total distance?
Example 2:
c) What is the acceleration in interval B?
Constant velocity of +40 m/s
d) What is the distance traveled during t=20s to t = 40s?
The distance covered is the “area under” the line.
Area = (b)(h)
Distance = (20s)(40m/s)
Distance = 800m
e) What is the total distance?
Distance = 400m + 800m = 1200m

18. Acceleration Graph
m/s2 vs second

19. Graph Summary

20. d vs t graph also referred to as a position time graph
Slope of line is velocity
Linear line represents a constant velocity
Horizontal line represents no motion
Curved line represents acceleration
Steeper slope represents greater velocity
Slope = Dd /Dt = velocity
Distance from detector CAN be indicated

21. v vs t graph Slope of line is acceleration
Linear line represents uniform acceleration
Horizontal line represents constant velocity, a=o
Curved line represents changing acceleration
Steeper slope represents greater acceleration
Slope = Dv /Dt = acceleration
Distance from detector cannot be indicated, only direction: away is positive and towards is negative
Area under curve indicates displacement

22. a vs t graph Linear line– acceleration is changing at a constant rate
Horizontal line– uniform acceleration(the acceleration stays the same)
Curved line– acceleration is changing non-uniformly
Steeper slope-- greater change in a
Slope = Da /Dt
Area under curve indicates velocity

23. Comparing graphs No motion (v=0)

24. Constant Velocity (a=0) positive direction

25. Constant velocity (a=0) negative direction

26. Describing Motion with graphs
Classwork: Graphing Little Dudes WS # 2