3. SCALAR
A scalar has a numerical quantity only.
Examples
Distance
55km
Temperature
30° c
Time
32 seconds
Anything else
9000 points
4. VECTORS
Vectors, unlike scalars, have both a magnitude and a
direction.
Examples
1D displacement
-22m
+63km
2D displacement
22m northeast
63km north
5. REPRESENTING A VECTOR
Represented by scaled vector diagrams
Arrow pointing in specific direction
Scale listed
Magnitude of vector labelled (arrow drawn according to
scale)
Direction of vector labelled (degrees)
Eg.
6. DIRECTION OF VECTOR
The direction of vector is the anti-clockwise angle of
rotation which the vector makes with due East
7. THE RESULTANT
The vector sum of all the individual vectors.
The result of combining the individual vectors
together
Determined by adding the individual forces together
using vector addition methods.
The direction of a resultant vector can often be
determined by use of trigonometric functions.
Can also be obtained by the head to tail method(best
method).
9. DETERMINING RESULTANT
(GRAPHICALLY)
Resultant=sum of 2 or more vectors.
By drawing a graph we can tell the resultant of 2 or more vectors.
For example, given
By moving B to the end of A, and C to the end of B, we can tell the total
distance and direction.
We can get the resultant by drawing a line from the start to
the end of C.
10. EXAMPLE OF THE HEAD TO TAIL
METHOD
Two different vectors add up to form… The Resultant!
11. DETERMINING RESULTANT
(MATHEMATICALLY)
Car A travels 6m eastwards and 8m northwards.
a)What is its displacement towards the northeast?
b)What is the direction of vector from car A’s starting
point?
Displacement = sqrt(6²+8²)
= sqrt(100)
= 10
Direction = sin ¹(8÷6)⁻
= 53.1°
12. SAMPLE QUESTION
A car travels 300m North from point A to point B,
turns 90° clockwise and travels a further 400m to
point C.
a)What is the total distance he has travelled?
b)What is his total displacement?
AB = 300m
BC = 400m
AB+BC=AC
300m+400m=700m
The total distance is 700m
13. SAMPLE: PART B)
To illustrate it better, we need a diagram.
A
B
300m
400m C
?m
14. SAMPLE: PART B)
B 400m C
?m
A
300m
Through Pythagoras's theorem:
AB²+BC²=AC²
AC=√AB²+BC²
AC=√2500m
= 500m
Angle A= tan-1
(400/300)
= 53.1°
Therefore:
The car’s displacement is 500m to 53.1° NE.
500m
