Transcript Representing Motion Motion diagrams, the particle model and position vs. time graphs….

Representing Motion
Motion diagrams, the particle model
and position vs. time graphs….
Motion Diagrams: Photo #1
1
Motion Diagrams: Photo #2
2
Motion Diagrams: Photo #3
3
Motion Diagrams: Photo #4
The Motion Diagram
Motion Diagram of a Bird
Adding a Coordinate System
Particle Model Showing Position
Motion Diagram Showing Negative Position
Representing Motion Quantitatively

Displacement = change in position
d = df – di
Change in position is equal to the final position minus initial
position. Answer may be negative, indicating a final position
that is negative in relation to the initial position.
Representing Motion Quantitatively

Time Interval
t = tf – ti
The time interval is equal to the final time minus the initial time.
The answer is always positive in our dimension.
Average Velocity
d d f  di
v

t
t f  ti
Average velocity is defined as the change in position, divided
by the time Interval during which the change occurred. This
variable is bold to indicate that it is a vector quantity,
possessing both magnitude and direction. Answer can be
negative, indicating a direction opposite to what is established
as positive.
Average Speed

Average speed =
v
The average speed is equal to the absolute value of
the average velocity. The combination of an
objects average speed, and the direction in which it
is moving is the average velocity.
Position-Time Graph of the Runner
HW #1. What is the position of the runner at 4.5 seconds?
HW #2. How long to 30.0 m?
Graphing Techniques:

Identifying the independent and
dependent variable:
Independent: The factor that is changed or
manipulated during the experiment. Plotted
on x-axis.
 Dependent: Depends on the independent
variable. Plotted on y-axis.

Graphing Directives:

Always use the graphing directives in
your appendix for plotting graphs.
HW #3: Plot the Data:
Length of a Spring for Different Masses
Mass Attached to Spring (g)
Length of Spring (cm)
0
5
10
15
20
25
30
35
13.7
14.1
14.5
14.9
15.3
15.7
16.0
16.4
Relationships in Data

Linear Relationships:
When the ‘line (curve) of best fit’ is a
straight line, the dependent variable varies
linearly with the independent variable.
 Relationship can be described as:
y = mx + b
The slope will be the change in the
dependent variable as to the change in the
independent variable.

Relationships in Data

Non-Linear Relationships:

Two of the most common are the quadratic
and inverse relationships. The quadratic
type exists when one variable depends on
the square of another.

We will discuss graphs of this type in a
future lab.
Calculating Velocity or Speed
From a Graph

To calculate velocity or speed from a
linear position vs. time graph:
Find the slope of the line!
Calculating Velocity or Speed
from a Graph with Slope
Find two points on the line: P1 and P2
 Identify the x and y coordinates of both
points: (x1,y1) and (x2,y2)
 Plug in the variables for the slope
formula: y2-y1/x2-x1 = slope = velocity

Position-Time Graph of a Car
HW #4. This car is moving in a negative direction at
what speed?
HW #5. What is this car’s velocity?
HW #6. Describe the Motion of Two
Pedestrians:
HW #7. Describe the Motion of
Runner A and Runner B:
HW #8. Rank Average Speed from
Greatest to Least. Any Ties?