1. Motion
Goal 2

2. Motion The change in position Two types
1. Scalar Quantities: no direction is indicated
Example: the dog walked 5 meters
2. Vector Quantities: direction is indicated
Example: the dog walked 5 meters east
Directions: North, East, South, West

3. Distance and Displacement
Distance: how far (in meters) an object travels
Displacement: the change in position of an object.

4. Displacement Along a Straight Line
You can calculate displacement using the formula:
∆d=df-di
∆d=displacement
df= final position
di= initial position

5. Calculating Displacement
To determine displacement, draw a number line.
If you move to the right, your displacement is positive or east
If you move to the left, your displacement is negative or west.

6. Calculating Displacement
Ex. di= 3
df= 7
So, the change or ∆ in d= 4 because 7-3=4

7. Examples
Ex. di= -2
df= 7
What’s ∆d??

8. Distance vs. Displacement
Distance: a scalar quantity
Displacement: a vector quantity
A straight line that connects the origin and the final destination
You must indicate the direction of the displacement
Origin (O)
5 Meters
Final (F)
7 Meters
Southeast (SE)

9. Calculating Displacement in Different Directions
Calculate the total distance by adding all given distances.
Draw the diagram on graph paper using the scale: 1unit = 1 square
Draw in displacement arrow (from beginning of 1st arrow to the end of the last arrow)
Use Pythagorean Theorem to solve for displacement.

10. Distance vs. Displacement
Origin (O)
5 Meters
Final (F)
7 Meters
Southeast (SE)

11. How to Use Pythagorean Two different situations:
1. If you have a right triangle (2 arrows total):
A2+B2=C2
A= Distance of 1st vector (arrow)
B= Distance of 2nd arrow
C= Final distance of displacement arrow

12. Distance vs. Displacement
Right triangle
Origin (O)
5 Meters
Final (F)
7 Meters
Southeast (SE)

13. How to Use Pythagorean Next, solve for C.
To do this, you have to plug your numbers into the equation (A2+B2=C2 )
A=5
B=5
C2=?
= C2
25+25= C2

14. How to Use Pythagorean
To get rid of the square in C2 , you must take the square root of both sides!
√25+25=√C
√50= 7.07m
So, the final displacement is 7m, SE

15. Distance vs. Displacement
Right triangle
Origin (O)
5 Meters
Final (F)
7 Meters
Southeast (SE)

16. How to Use Pythagorean
2nd situation is when you have more than 2 arrows.
For example: You walk 5 meters north. You then walk 3 meters east. Next, you walk 2 meters south.
Calculate distance the same way as well as draw it out on the graph and draw in your displacement arrow.

17. How to Use Pythagorean
You will not have a right triangle, so you must make one with the lines you have drawn.
3 Meters
2 Meters
5 Meters

18. How to Use Pythagorean
Now that you have a right triangle, you must determine the length of the sides.
The top is 3 m since it is the same length as the other top line.
The left side was originally 5m, but now you need to subtract 2, so it is 3 m long.

19. How to Use Pythagorean Next, plug values into the equation: A2+B2=C2
A=3m
B=3m
C2=?
= C2
9+9=C2
√18=√C
ANS= 4.24 meters, SW