2. Scalars and Vectors
A scalar quantity has a size
and unit.
E.g. 16 N (Newtons)
A vector quantity has a size,
unit and direction.
E.g. 5 km/h [N] (North)
3. Distance and Displacement
Distance travelled depends on
position.
Distance is a scalar quantity.
It is always positive.
E.g. d = 5 km
4. Distance and Displacement
Displacement depends on the
new position compared to the
old position.
Displacement is a vector
quantity.
E.g. Δd or đ = 5 km North
5. Exam Question
The following graph represents the trail followed by a hiker going from A to F (A –> B –> C –> D –
> E –> F). One centimetre represents 100 metres.
What is the displacement of the hiker?
A) 1 700 m
B) 700 m
C) 500 m
D) 200 m
9. Cardinal and Degrees
[N 45 ° E] means you start at
North and turn 45 ° East.
It is also known as NE.
Or as 45 °
10. Vector Addition
We can show vectors as
arrows in diagrams.
We add vectors tip to tail.
Vector Ả +Vector B = Vector B + Vector Ả
The result of adding two or more vectors is the
RESULTANT VECTOR.
Vectors are written with little arrows on top.
14. Multiplying Vectors
Multiplying vectors only
changes magnitude not
direction (if positive).
ā = (1,2); 3 ā = (3,6)
đ = 5 km 45°;
2đ = 10 km 45°
15. Vector Division
It is just like vector
multiplication, but with a
fraction.
N.B. multiplying by a negative
ř = (3,2); - ř = (-3,-2)
Ŝ = 2 m [N]; -ŝ = 2m [S]
16. x-Component of a Vector
ā-hyp opp
Θ y-part
adj x – parts
Cos θ = adj/hyp = x/ā
Thus, x = ā cos θ
17. y-Component of a Vector
ā-hyp opp
Θ y-part
adj x – parts
sin θ = opp/hyp = x/ā
Thus, y = ā sin θ
18. Addition of Vectors:
Component Method
Add the x-components of the
vectors together.
Add the y-components of the
vectors together.
Add the total x vector to the
total y vector tip to tail.
19. Tools for Solving
You can use diagrams;
Pythagoras c2 = a2 + b2;
Sine Law
Cosine Law
SOHCAHTOA
20. Summary
Some motions can be seen
easily; other motions must be
observed using other senses
or devices.
The trajectory is the path of a
moving object.
21. Summary
Vector quantities have
magnitude and direction.
Scalar quantities only have
magnitude.
Displacement, or change in
position, is a vector quantity.
22. Summary
Distance, the path length, is a
scalar quantity.
Add vectors tip to tail.
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