1. Motion in One Dimension Position, Displacement and Velocity
WHS Physics

2. Essential Questions What is Motion? What is motion in one dimension?
What is Displacement?
What is velocity?
How do speed and velocity differ?
How can you determine an objects velocity?
How are velocity and displacement related… graphically?

3. Motion The study of objects in motion is the foundation of Physics.
Striving to understand the motion and interaction of objects and particles has led to our deepest understanding of matter and energy
The study of objects in motion is called Kinematics

4. What is Motion?
Motion is simply the displacement of an object that takes place over time
Displacement is the change in the position of an object

5. One–Dimensional Motion
Motion can occur in any direction or dimension…
up or down, left or right, forward or backward
One-Dimensional (1-D) motion is the simplest form of motion
In 1-D motion, movement is restricted to only one direction… Like a train on a track
Many real-world situations can be modeled in 1-D, so 1-D motion is a good place to start studying Kinematics

6. Displacement But, where do you start…?
When an object moves from one point to another, its displacement is the straight line from the starting point to the ending point.
But, where do you start…?

7. Displacement
To measure displacement, you need to establish a frame of reference
A frame of reference is a relatively fixed point or set of axes from which you can measure the position and motion of objects
In day to day experience, you are your own frame of reference
What would be a good frame of reference for studying the motion of our planets?

8. 1-D Motion
In 1-D motion, we can establish our frame of reference as the “x-axis” (or “y”) to measure displacement and motion -1 1 2 3 4 5 6 X

9. xi xf Displacement equals the change in position-1 1 2 3 4 5 6
X (meters) xi xf
Displacement equals the change in position
Using our reference, displacement equals the “change in x”
Symbol “D” denotes change in a variable

10. + - Displacement Displacement can be positive or negative -1 1 2 3 4 5-1 1 2 3 4 5 6
X (meters) + -

11. Displacement
Displacement is not always equal to the actual distance traveled
Distance depends on path traveled, not on final position B A C -1 1 2 3 4 5 6
X (meters)

12. To get a better picture, we need to relate position to time…
Displacement
If the car is in motion, displacement doesn’t really tell us much about what is happening.
To get a better picture, we need to relate position to time… -1 1 2 3 4 5 6
X (meters) xi xf
The car is in motion
Based on our reference frame it is moving from xi to xf
Its displacement equals Dx = xf – xi

13. Instantaneous Position-1 1 2 3 4 5 6
X (meters) xi xf
Even though the car is moving, we can identify the instant it is at a certain position by reading a clock
At ti, the car is at xi… At tf, the car is at xf
At a given time, t, the position of a moving object is called an Instantaneous Position… Why?

14. Average Velocity t1 x1 t2 x2 . tf xf Time Position
If you plot an objects instantaneous position versus time, you can determine graphically an objects position at any given time
Time
Position

15. Average Velocity What are the units of the slope of this line? t1 x1
Time
Position t1 x1 t2 x2 . tf xf
If you plot an objects instantaneous position versus time, you can determine graphically an objects position at any given time
Time
Position

16. Average Velocity
Position xf xi tf ti
Time

17. Average Velocity t = ti t = tf xi xf-1 1 2 3 4 5 6
X (meters) xi xf
V = Dx / Dt… Why is this called the average velocity?
Can Dt be negative?
Can velocity be negative?

18. + - Velocity versus Speed Displacement can be positive or negative
Since Dx can be negative, velocity can be negative… ie, the opposite direction
Speed is the rate at which something moves
Velocity is speed in a given direction -1 1 2 3 4 5 6
X (meters) + -

19. Constant Velocity
If the average velocity is the same for all time intervals then the object is moving at Constant Velocity

20. Instantaneous Velocity
If the average velocity changes from one time interval to the next, the velocity at any given time is called the Instantaneous Velocity

21. Instantaneous Velocity

22. What we know… What is velocity? How do speed and velocity differ?
How can you determine an objects velocity?
How are velocity and displacement related… graphically?

23. What we know… What is Motion? What is motion in 1 dimension?
Motion is simply the displacement of an object that takes place over time
What is motion in 1 dimension?
In 1-D motion, movement is restricted to only one direction… Like a train on a track
What is Displacement?
Displacement is the change in the position of an object

24. Questions?