1. Distance, Direction and Position
Chapter 12

2. Chapter Twelve: Distance Direction and Position
12.2 Speed
12.3 Graphs of Motion
California 8th Grade Science Standards Addressed
1. The velocity of an object is the rate of change of its position. As a basis for understanding this concept:
Students know position is defined in relation to some choice of a standard reference point and a set of reference directions.
Students know that average speed is the total distance traveled divided by the total time elapsed and that the speed of an object along the path traveled can vary.
Students know how to solve problems involving distance, time, and average speed.
Students know the velocity of an object must be described by specifying both the direction and speed of the object
Students know changes in velocity may be due to changes in speed, direction, or both
Students know how to interpret graphs of position versus time and graphs of speed versus time for motion in a single direction

3. Positive and Negative Position
Investigation 12A
Positive and Negative Position
How do we measure position in two dimensions?

4. 12.1 The position variable
Position is a variable and it is always relative to an origin, or the place where the object’s starting point was zero.

5. Distance

6. 12.1 The position variable
Motion is about knowing where things are and how they move.
To understand where things are, we need to understand position.

7. 12.1 Forward and backward
Position and distance are similar but not the same.
Both use units of length.
Distance can have only positive values.

8. 12.1 Forward and backward Position uses positive and negative numbers.
Positive numbers are for positions to the right (in front) of the origin.
Negative numbers are for positions to the left (or behind) the origin.

9. 12.1 Forward and backward Many variables can be positive or negative.
These include position, speed, and force.
These variables are called vectors because they can have a value and a direction.
We use the term velocity to mean speed with direction.

10. 12.1 Keeping track of where you are
Curiosity is a rover sent to explore Mars.
It landed on Mars in 2012.
Where is Curiosity now?

11. Curiosity – Where is it now?

12. 12.1 Keeping track of where you are
Curiosity keeps track of its velocity vector and uses a clock.
Suppose Curiosity moves forward at 0.2 m/s for 10 seconds.
What is Pathfinder’s velocity?

13. 12.1 Keeping track of where you are
Suppose Pathfinder goes backward at 0.2 m/s for 4 seconds.
What is Pathfinder’s velocity?
What is Pathfinder’s change in position?

14. 12.1 Keeping track of where you are
The change in position is the velocity multiplied by the time.

15. 12.1 Keeping track of where you are
Each change in position is added up using positive and negative numbers.
Curiosity has a computer to do this.

16. 12.1 Maps and coordinates
If Curiosity was crawling on a straight board, it would have only two choices for direction.
Out on the surface of Mars, Curiosity has more choices. The possible directions include north, east, south, and west, and anything in between.

17. 12.1 Maps and coordinates
Curiosity’s exact position can be described with two numbers.
These numbers are called coordinates.
This graph shows Curiosity at coordinates (4, 2) m.

18. 12.1 Maps and coordinates This kind of graph is called a map.
The graph can also show any path Curiosity takes, curved or straight.
This kind of graph is called a map.
Street maps often use letters and numbers for coordinates.

19. 12.1 Vectors on a map Where are you compared to where you started?
Suppose you run east for 10 seconds at a speed of 2 m/s.
Then you turn and run south at the same speed for 10 more seconds.
Where are you compared to where you started?