1. Physics 131
9/9/15
Vectors
Each point in space is specified by three numbers: (x, y, z), and a position vector– an arrow showing the displacement from the origin to that position.
Vectors add like successive displacements or algebraically by
Prof. E. F. Redish

2. Physics 131
Notation
9/9/15
We specify the directions we are talking about by drawing two little arrows of unit length in two perpendicular directions.
“x” and “y” are called the coordinates and can be positive or negative.
Note that if x is negative, it means is a vector pointing in the direction opposite to
Prof. E. F. Redish

3. Velocity Average velocity is defined by
Physics 131
9/9/15
Velocity
Average velocity is defined by
Instantaneous velocity is what we get when we consider a very small time interval (compared to times we care about)
Note: an average velocity goes with a time interval.
Note: an instantaneous velocity goes with a specific time.
Prof. E. F. Redish

4. Vectors (2-D coordinates)
Physics 131
9/9/15
Vectors (2-D coordinates)
We have 2 directions to specify. We must
Choose a reference point (origin)
Pick 2 perpendicular axes (x and y)
Choose a scale
We specify our x and y directions by drawing little arrows of unit length in their positive direction.
A position vector (displacement from the origin) is written
x and y have units, do not.
Prof. E. F. Redish

5. 1D Velocity Velocity is the rate of change of position
Average velocity
= (how far did you go?)/(how long did it take you?)
Instantaneous velocity = same (but for short Δt)

6. Graphing velocity: Figuring it out from the position
Physics 131
9/9/15
Graphing velocity: Figuring it out from the position
Slope
= <v>
You can figure out the velocity graph from the position graph using Δx Δt
v (m/s)
9/9/15
Prof. E. F. Redish

7. Physics 131
9/9/15
Position to velocity
Ratio of change in position that takes place to the (small) time interval
Difference of two positions at two (close) times
9/9/15
Prof. E. F. Redish

8. Recall: Vectors (2-D coordinates)
Physics 131
9/9/15
Recall: Vectors (2-D coordinates)
We have 2 directions to specify. We must
Choose a reference point (origin)
Pick 2 perpendicular axes (x and y)
Choose a scale
We specify our x and y directions by drawing little arrows of unit length in their positive direction.
A position vector (displacement from the origin) is written
x and y have units, do not.
Prof. E. F. Redish

9. Vector velocity and speed
A displacement – a change in position – has a direction. This means velocity = displacement/time interval has one too.
We define speed as the magnitude of velocity. (No vector on this. Why?)

10. Physics 131
9/9/15
Velocity to position
change in position that takes place in a small time interval
sum (“Σ”) in the changes in position over many small time intervals
9/9/15
Prof. E. F. Redish

11. What have we learned? Representations and consistency
Physics 131
9/9/15
What have we learned? Representations and consistency
Visualizing where an object is  a position graph at different times
Visualizing how fast an object is moving  a velocity graph at different times
Position graph  velocity graph
Velocity graph  position graph
slopes
areas
Prof. E. F. Redish

12. Vectors
If a position vector (displacement from the origin) lies in each of the four indicated quadrants, what can you say about the vector representation of that displacement,
x and y are both positive
x and y are both negative
x is positive and y is negative
x is negative and y is positive y D A x C B