1. Scalars/Vectors and Distance/Displacement

2. Characteristics of a Scalar Quantity
Only has magnitude
Requires 2 things:
1. A value
2. Appropriate units
Ex. Mass: 5kg
Temp: 21° C
Speed: 65 mph

3. Characteristics of a Vector Quantity
Has magnitude & direction
Requires 3 things:
1. A value
2. Appropriate units
3. A direction!
Ex. Acceleration: 9.8 m/s2 down
Velocity: mph West

4. More about Vectors A vector is represented on paper by an arrow
1. the length represents magnitude
2. the arrow faces the direction of motion
3. a vector can be “picked up” and moved on
the paper as long as the length and direction
its pointing does not change

5. Graphical Representation of a Vector
The goal is to draw a mini version of the vectors to give you an accurate picture of the magnitude and direction. To do so, you must:
Pick a scale to represent the vectors. Make it simple yet appropriate.
Draw the tip of the vector as an arrow pointing in the appropriate direction.
Use a ruler & protractor to draw arrows for accuracy. The angle is always measured from the horizontal or vertical.

6. Understanding Vector Directions
To accurately draw a given vector, start at the second direction and move the given degrees to the first direction. N
30° N of E W E
Start on the East origin and turn 30° to the North S

7. Distance Distance – the length traveled by an object
Practice – What is the distance?
Pattie walks 4 km North, then 3 km East
Joe runs 30 m East, then runs 40 meters West
Aaron jogs 4 km East, 4 km North, 4 km West, and 4km South
Answers: 7 km ; 70 meters ; 16 km

8. Distance vs. Displacement
Distance – length
Displacement – distance AND direction of a movement from the starting point
Distance vs. Displacement

9. If an object moves in a single direction, the displacement equals the distance + the direction
4 km
total displacement =
4km North
start here 

10. If an object moves in two opposing directions, the displacement is the difference between the two.
total distance = = 7 km
3 km
4 km
Displacement can be positive or negative. A negative direction can be either the opposite of the original movement, or can follow the sign of a typical graph [North/East vs South/West]
start here 
total displacement =
4 km North + -3 km South = 1 km North
(of original starting point)

11. If an object moves in two directions, a triangle will be formed
If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a2 + b2 = c2 to solve.
Displacement – cont’d
3 km
4 km
displacement
start here 

12. If an object moves in two directions, a triangle will be formed
If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a2 + b2 = c2 to solve.
Displacement – cont’d
3 km
displacement =
= c2
c2 = (16) + (9) = 25
c2 = √(25)
c = 5km
5 km
4 km
start here 

13. Displacement – cont’d Displacement can be given in:
units with direction
example: x number of meters North
30 meters East + 40 meters West
displacement = 10 meters West

14. Displacement – cont’d Displacement can be given in:
positive or negative units [like on a graph]
positive = North {up} or East {right}
negative = South {down} or West {left}
30 meters east + 40 meters west = 30 meters + (-40) meters = -10 meters

15. Displacement Practice – What is the displacement?
Pattie walks 4 km North, then 3 km East
5 km displacement
Joe runs 30 m East, then runs 40 meters West
10 meters [or -10] displacement
Aaron jogs 4 km East, 4 km North, 4 km West, and 4km South
0 meters displacement
Displacement
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