1. Motion in One Dimension
Chapter 2
Motion in One Dimension

2. Motion in One Dimension
Leading Question: What is one dimensional motion?
Answer: The simplest form of motion
i.e. a train moving on a track can only move back and forth

3. You in motion Try to think of all the ways you’re moving right now
Earth is rotating on its axis
Earth is revolving around the Sun
The solar system is orbiting the Milky Way
So….how can we really come up with a simple way to describe an object’s motion?

4. Frames of Reference
A frame of reference: A coordinate system for specifying the precise location of objects in space
So what could be a frame of reference for a train?
Stations along track
Any frame of reference can be chosen as long as you’re consistent

5. Displacement
What is displacement?
A change in position

6. Displacement Eqn
Displacement= change in position= final position – initial position
Since displacement is relative to the starting position, direction is
necessary!

7. The Sign of displacement indicates direction !
In your book (unless otherwise stated) motion to the right or up is positive and motion to the left or down is negative

8. Sign Conventions Positive Directions Negative Directions Up Down Right
Left
North
South
East
West

9. Displacement isn’t the same as distance traveled
Say you went from your friend’s house to the grocery store. What would be your displacement? What is your distance traveled?

10. The distance traveled would be 6.4 miles.
The displacement would be 6.4 miles East (or to the right).
You must include direction!
Now say you traveled from your friend’s house to the grocery store and then returned to your friend’s house. What is your distance traveled and what is your displacement?

11. Distance vs Displacement
Distance traveled: 6.4 mi mi = 12.8 mi
Displacement: 0 mi! Because final position = initial position.

12. Velocity
Average velocity is the change in position divided by change in time.
Average velocity can be positive or negative!!

13. Example
During a race, Andra runs with an average velocity of 6.02 m/s to the east. What is Andra’s displacement in 137 s?
Notice that the velocity is positive which means that east is positive.
Rearrange the displacement equation:
Plug in your values and solve:
= (6.02 m/s)(137 s)= 825 m to the east

14. Velocity is not the same as speed
Average Speed = distance traveled
time of travel
Average Velocity= displacement
VELOCITY HAS DIRECTION. SPEED DOES NOT.

15. What information does the graph show?
How would you calculate the slope of the line?
Slope = rise = change in vertical coordinates
run change in horizontal coordinates
Slope = Δx = AVERAGE VELOCITY!!! Δt
So the moral of the story is….THE SLOPE OF AN OBJECT’S POSITION VS TIME GRAPH = THE AVERAGE VELOCITY OF THE OBJECT

16. Instantaneous Velocity
Instantaneous velocity of an object is the velocity at some instant…so it can be different than average velocity
To calculate instantaneous velocity you need to measure the slope of a line that is tangent to the graph at that instant.