1. Distance & Displacement
How much did you travel from your house to your friend’s house?
8.2 km km km = 14.5 km
so, distance is 14.5 km.
Where is your friend’s house located as compared to your house?
2.7 km at 4o W of N
so, displacement is 2.7 km at 356o E of N

2. What is a Vector?
A vector is an arrow. A vector has a starting point (Tail) and an ending arrow(Head) .
Head
magnitude Ɵ
Tail
reference direction
A vector has magnitude (size) and direction (angle in o formed with a reference direction).

3. Distance & Displacement
Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below:
Distance d is a scalar quantity (no direction): A B
d = 20 m
Contains magnitude only and consists of a number and a unit.
(20 m, 40 mi/h, 10 gal)

4. Displacement—A Vector Quantity
Displacement is the straight-line separation of two points in a specified direction. N
A vector quantity:
Contains magnitude AND direction, a number, unit & angle.
(12 m, 200 N of E) A B
D = 12 m, 20o q E

5. Distance & Displacement
Displacement is the straight-line separation of two points in a specified direction (arrow).
A vector quantity:
Contains magnitude AND direction, a number, unit & angle.
(12 m, 300; 8 km/h, N) A B
d = 12 m, 20o q

6. Q: Displacement vs. distance.𝜃
1. What is distance?
distance= = 11 blocks
2. What is displacement (magnitude & angle)?
𝑅= ≅8.5 𝑏𝑙𝑜𝑐𝑘𝑠
𝜃= 𝑡𝑎𝑛 − = 21 𝑜
𝑡𝑎𝑛𝜃= 𝑜𝑝𝑝. ℎ𝑦𝑝. = 3 8
N of E

7. Distance & Displacement
For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W.
Net displacement d is from the origin to the final position: d
8 m,E x
x = -4
x = +8
d = 4 m, W
12 m,W
What is the distance traveled?
20 m !!