1. 2.2 Where and When? Essential Questions What is a coordinate system?
How does the chosen coordinate system affect the sign of objects’ positions?
How are time intervals measured?
What is displacement?
How are motion diagrams helpful in answering questions about an object’s position or displacement?
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Where and When?

2. 2.2 Where and When? Vocabulary New Review coordinate system origin
Dimension
New
coordinate system
origin
position
distance
magnitude
vector
scalar
time interval
displacement
resultant
Vocabulary
Where and When?
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3. 2.2 Where and When? 1. Coordinate Systems
a. A coordinate system tells you the location of the zero point of the variable you are studying and the direction in which the values of the variable increase.
b. The origin is the point at which both variables have the value zero.
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Where and When?

4. 2.2 Where and When? 1. Coordinate Systems
Consider a runner on this coordinate system.
c. You can indicate how far away an object is from the origin at a particular time by drawing an arrow from the origin to the object.
The two arrows locate the runner’s position at two different times.
d. Position is the distance and direction from the origin to the object.
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5. 2.2 Where and When? 2. Vectors and Scalars
a. Quantities that have both size (also called magnitude) and direction are called vectors.
b. Vectors can be represented by arrows.
Position is an example of a vector. It is represented by the symbol x.
2. Vectors and Scalars x1 x2
Where and When?
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6. 2.2 Where and When? 2. Vectors and Scalars
c. A quantity that is just a number without any direction is a scalar.
d. Examples of scalars:
Time
Distance
Temperature
e. Is mass a scalar? Explain.
Yes. Mass has a magnitude, but no direction.
2. Vectors and Scalars
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7. 2.2 Where and When? 2. Vectors and Scalars
f. The difference between two times is called a time interval.
1). Time intervals are scalars.
2). The time interval is defined mathematically as follows:
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8. 2. Vectors and Scalars ∆x = xf − xi
g. A change in position is called a displacement.
1). Displacement is a vector. It is drawn with its tail at the earlier position and its tip at the later position.
2). Displacement can be represented mathematically as
∆x = xf
− xi xf xi ∆x
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9. 2. Vectors and Scalars
h. A vector that represents the sum of two other vectors is called a resultant.
1). Example of Vector Addition
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10. 2. Vectors and Scalars 2). Example of Vector Subtraction
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11. 2. Vectors and Scalars 3). Example of Vector Subtraction
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