1. Chapter 2: Reference Frames, Diplacement, and Velocity
Sections 2-1 to 2-3
Pages 20-23

2. Key Formulas

3. 2-1 Reference Frames and Displacement
Any measurement of position, distance, or speed must be made with respect to a reference frame.
For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher.
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4. 2-1 Reference Frames and Displacement
Motion is described in many ways:
Distance
Velocity
Displacement
Acceleration
Speed
Direction
But ALL of this depends on your point of view, or frame of reference.
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5. 2-1 Reference Frames and Displacement
When we describe motion, it is important to not only describe its speed, but also its direction.
We can always choose to place the origin (0,0) and the x & y axes as we’d like
However, we usually choose +x to the right and –x to the left.
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6. 2-1 Reference Frames and Displacement
The displacement is written: ∆x = x2 − x1
Left: Displacement is positive. Right: Displacement is negative.
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7. 2-1 Reference Frames and Displacement
We make a distinction between distance and displacement. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path.
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8. 2-1 Reference Frames and Displacement
What distance has been traveled?
What is the displacement?
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9. 2-1 Reference Frames and Displacement
Question: If you go to get a drink during class, what is the distance that you’ve traveled? What is your displacement?

10. 2-1 Reference Frames and Displacement
Since displacement has both magnitude (number) and direction, it is represented by a vector:
A vector is shown as an arrow.

11. 2-1 Reference Frames and Displacement
Figure 2
Figure 1
Determine the displacement for each Figure: Figure 1: Figure 2:

12. 2-2 Average Velocity
Speed: how far an object travels in a given time interval Velocity includes directional information:
(2-1)
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13. 2-2 Average Velocity
Velocity tells us both magnitude (numerical value) and direction (+ or -):
So…..Velocity is a VECTOR!!
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14. 2-2 Average Velocity Let’s look at the example from earlier:
Determine the speed:
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15. 2-2 Average Velocity Let’s look at the example from earlier:
Determine the velocity:
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16. 2-2 Average Velocity So, average velocity is calculate:
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17. 2-2 Average Velocity
Example Problem: During a 3.00 s time interval, the runner’s position changes from x1 = 30.0 m to x2 = 10.0 m. What was the runner’s average velocity?
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18. 2-2 Average Velocity
Video Problem: Determine the average velocity of the runner up the hill.
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19. 2-3 Instantaneous Velocity
The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short.
These graphs show (a) constant velocity and (b) varying velocity.
(2-3)
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20. 2-3 Instantaneous Velocity
Instantaneous speed always equals instantaneous velocity (apart from direction) since when time is infinitesimally small, distance = displacement.