### Linear Motion Displacement vs. Distance Displacement = vector

```Principles of Physics

motion along a straight line path, motion in
one dimension
 Which way are you headed?
 How far did you go?
 How fast are you going?
Direction
 In order to get anywhere you need to know
 North, South, West , East
 Up, Down, Left , Right

Direction can also be negative or positive for
math purposes
 Negative: South, West, Down, Left
 Positive: North, East, Up, Right
Almost all quantities have units
- examples: meters, seconds, kilograms
- Without units numbers would be meaningless
Vector – Quantities that include a direction
 Vectors can be drawn
 They are represented by arrows
Example: 12 m south
Scalar – Quantities that do not include direction
Example: 4 seconds
How far did you go?
Path length (p): total length of path taken
- measured in meters(m)
- scalar quantity (does not include direction)
2m
1m
6m
8m
p=8m+6m+2m+1m
p = 17 m
How far did you go?
Displacement (d): change in position, shortest path between
start and finish
- vector (amount and direction)
2m
1m
6m
8m
6m
3m
Path Length = 9 m
Displacement =
9 m right
3m
6m
Path Length = 9 m
Displacement =
3m
Path Length = 9 m
3 m left
Displacement =
?
a2  b2  c2
6m
6m2  3m2  c 2
c  6.71m
northeast

To determine displacement draw a diagram of the path taken
 Example: 8 m east, then 6m north, then 2 m east, then 1 m
2m
south
1m
6m
8m

Simplify the diagram to a right triangle
1m
6m
8m

2m
Use Pythagorean Theorem to determine the displacement
a2  b2  c2
10 m
5m
10m 2  5m 2  c 2
c  11.2m
northeast
Jan walks 4 meters north then turns to walk 4
meters east and finally turns to walk another 8
meters north. Determine Jan’s displacement.
a2  b2  c 2
8m
4m
8m
d
4m
4m
4m
12m   4m 
2
c  12.65m
northeast
2
 c2
Units for path length or displacement:
Standard Unit: meter
Anything else must be converted
 1 meter = 100 centimeters = .001 kilometer
 1 kilometer = 1000 meters
 1 meter = 3.28 feet
 1 kilometer = 0.6214 miles
Smaller unit to larger unit: divide


centimeters to meters: divide by 100
millimeters to meters: divide by 1000
Larger unit to smaller unit: multiply

kilometers to meters: multiply by 1000
Smaller unit to larger unit: divide
1. Change 40 centimeters to meters
40cm
 0.4m
100cm / m
Larger unit to smaller unit: multiply
2. Change 6.8 kilometers to meters
6.6km(1000m / km)  6,600m
```