1. Motion in One Dimension (Position vs. Time) Chapter 5.1

2. Distance, Position and Displacement
Distance: The distance that an object has moved irrespective of your starting position.
Ex. You walk 3 meters north and then walk 3 meters south. What distance have you traveled?
meters

3. Distance, Position and Displacement
Position: Where you are relative to a or point.
Ex.: You walk meters north.
Your position is meters from your starting or reference point.

4. Distance, Position and Displacement
Displacement: A measure in distance relative to a point that includes .
Ex.: You walk 3 meters north and then 3 meters south. What is your displacement?
meters.
Ex.: Your walk 3 meters north and 4 meters east. What is your distance traveled? What is your displacement?
Distance: meters.
Displacement: meters

5. Motion of Objects
To describe the motion of an object, what other information will we need other than position, distance or displacement?
If I have the object’s and , what can be determined about the object’s motion? or
Now, lets look at some data

6. 1. Collect Data

7. 2. Choose appropriate axes and plot the data.

8. 3. Draw a curve that provides a “best fit” to the points.

9. What information does the shape of the curve provide?
Straight line =
Changing curve = changing velocity ( ).
Time
Position
Constant Velocity
Position
Time
Changing Velocity

10. What information does the shape of the curve provide?
Positive
Negative
Time
Position
Time
Position
Decreasing
Position
Time
Position
Time
Increasing

11. Characterize the motion of the object from A to E.
in the positive direction. .
Time
Position A B C D E

12. What information does the slope of the curve provide?
sloped curve = movement in the direction.
Time
Position
Positive Direction
Time
Position
Negative Direction

13. What else does the slope tell us?
What is the motion described by each curve?
How does the velocity of each curve compare to one another?
A is
B is moving at the
as C, but their starting
is different.
D is moving than
B or C.
Time
Position A C B D

14. Analyzing motion of more than one object.
Two vehicles travel through a speed trap traveling at two different velocities.

15. Determining the slope of the curve.
1997 World Championships - Athens, Greece
Maurice Green
100 90 80
y = 11.65x R
= 1.00 2 70 60
Distance (m) 50 40 30 20
y = 1.13x
+ 4.08x R 2
= 1.00 10 2 4 6 8 10
Time (s)

16. Velocity determined from the slope of the curve.
Since m = :
v = m/s
1997 World Championships - Athens, Greece
Maurice Green
y = 11.65x R 2
= 1.00 30 40 50 60 70 80 90
100 4 5 6 7 8 9 10
Time (s)
Distance (m)
Slope =
m =
m =

17. Key Ideas
Although space exists in 3 dimensions, analysis of objects in motion can be limited to one dimension to simplify problems.
When graphing position vs. time, use the x-axis for and the y-axis for .
By analyzing the shape of a position vs. time graph, the relative motion of the object can be determined, i.e. constant velocity, acceleration, stationary.
The slope of the position vs. time graph provides the over the time interval.