The document discusses scalar and vector quantities. Scalars are measured with numbers and units, while vectors also include direction. Vectors are represented by arrows, with length indicating magnitude and direction of motion. Distance refers to the total path length between two points, while displacement is the shortest distance between initial and final positions, including direction. Displacement is a vector quantity that does not depend on the route taken. Vectors can be added by placing their tails together to find the resultant vector.

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What is a scalar?
Scalar quantities are measured with numbers and units.
length
(e.g. 102°C)
time
(e.g. 16cm)
temperature
(e.g. 7s)

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What is a vector?
Vector quantities are measured with numbers and units, but
also have a specific direction.
acceleration
(e.g. 30m/s2
upwards)
displacement
(e.g. 200miles
northwest)
force
(e.g. 2N
downwards)

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

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Distance and Displacement
• Distance (d) refers to the length of the
entire path that the object travelled.
(Length between two points)
• Displacement (s) refers to the shortest
distance between the object’s two
positions, like the distance between its
point of origin and its point of
destination.

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Comparing scalar and vector quantities

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• Distance = total length of travel
• Displacement = change in position =
final position – initial position or Δx = xf –
xi
• Displacement can be positive, negative,
or zero

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Displacement is how far a body is from its
original position, including its direction.
Displacement

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Distance = 50 miles
Displacement =
50 miles South East
?
Magnitude Direction
A
B

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Vector or scalar?

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Adding vectors
Displacement is a quantity that is independent of the
route taken between start and end points.
Any two vectors of the same type can be added in this way
to find a resultant.
Two or more displacement
vectors can be added
“nose to tail” to calculate a
resultant vector.
A
B C
resultant vector
If a car moves from A to B and then to C, its total
displacement will be the same as if it had just moved in a
straight line from A to C.

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Simplifying vectors
Because of the way vectors are added, it is always possible to
simplify a vector by splitting it into components.
A
B
C
Imagine that instead of traveling via B, the car travels via D:
D
The car has a final displacement of x miles east and y miles
north. This can be represented by (x,y).
x
y
Its displacement is the
same, but it is now much
easier to describe.
x component
y
component
How would you describe
the car’s displacement in
component terms?