1. In this section you will:
Define Vectors vs. Scalars.
Define time interval.
Define displacement.
Compare displacement to distance
Define and Compare Speed and Velocity
Section 2.1-1

2. Vectors and Scalars
Quantities that have both size, also called magnitude, and direction, are called vectors, and can be represented by arrows.
Quantities that are just numbers without any direction, such as distance, time, or temperature, are called scalars.
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3. Vectors and Scalars
To add vectors graphically, the length of a vector should be proportional to the magnitude of the quantity being represented. So it is important to decide on the scale of your drawings.
The important thing is to choose a scale that produces a diagram of reasonable size.
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4. Vectors and Scalars
The vector that represents the sum of the other two vectors is called the resultant.
The resultant always points from the tail of the first vector to the tip of the last vector.
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5. Time Intervals
The difference between the initial and the final times is called the time interval.
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6. Time Intervals
The common symbol for a time interval is ∆t, where the Greek letter delta, ∆, is used to represent a change in a quantity.
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7. Time Intervals The time interval is defined mathematically as follows:
Although i and f are used to represent the initial and final times, they can be initial and final times of any time interval you choose.
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8. Displacement
The change in position during the time interval between ti and tf is called displacement.
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9. Displacement
The length of the arrow represents the distance the runner moved, while the direction the arrow points indicates the direction of the displacement.
Displacement is mathematically defined as follows:
Displacement is equal to the final position minus the initial position.
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10. Displacement vs. distance
Displacement indicates distance traveled in a given direction. Because it includes direction it is a vector. Distance is a scalar because it does not require a direction.
The displacement vector is always drawn with its flat end, or tail, at the earlier position, and its point, or tip, at the later position.
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11. Practice Problem 1
Mike walked five miles south to his school then turned and walked 2 miles north.
A. Draw a motion Diagram.
B. What is the distance travelled?
C. What is the displacement?

12. Practice Problem 2
Mike drove 2 miles North, the turned and went 5 miles West before going an additional 6 miles south.
A. Draw a motion Diagram.
B. What is the distance travelled?
C. What is the displacement?

13. Review
Which statement describes best the motion diagram of an object in motion?
A. a graph of the time data on a horizontal axis and the position on a vertical axis
B. a series of images showing the positions of a moving object at equal time intervals
C. a diagram in which the object in motion is replaced by a series of single points
D. a diagram that tells us the location of the zero point of the object in motion and the direction in which the object is moving
Section 2.1-9

14. Speed and Velocity
Speed= Rate of change of distance
S= distance/time
Velocity= Rate of change of displacement
V= displacement/time

15. Speed can never be negative because there is no such thing as “negative” distance.
Velocity can be negative, a negative velocity represents a motion toward the reference point where the change in displacement is negative.
Nonlinear motions have speeds that are different than their velocities.

16. Instantaneous vs. Average Motion
Instantaneous Speed and Velocity are represent motions at an exact moment in time.
Average Speed and Velocity represents an average motion over a specified amount of time.

17. Motion Graphs Example

18. A race car drives 500 miles over 3 hours on a circular track.
A- What is the average speed of the race car?
B- What is the average velocity of the race car?