1. Graphical Interpretation of Motion in One Dimension

2. Why Graphs?
Graphing gives us a visual “picture” of a mathematical relationship
Slopes of lines, x- or y-intercepts, and areas under curves have meaning
As determined by the equation representing the physical quantity

3. Graphing Tips Label axes (including units) Scale
Appropriate size to allow analysis
Mark scale on axes
Draw a line of “best fit”
Don’t simply connect the dots!!

4. Line of Best Fit • • • • Analyze data based on “best fit” •
Displacement (m) • •
Analyze data based on “best fit” •
Time (s)

5. Describe the motion of this object30 20
Displacement (m) 10
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Time (s)
Describe the motion of this object

6. Graphical Interpretation of Velocity
Velocity can be determined from a position-time graph
Average velocity equals the slope of the line joining the initial and final positions
An object moving with a constant velocity will have a graph that is a straight line

7. Average Velocity, Constant
The straight line indicates constant velocity
The slope of the line is the value of the average velocity

8. Average Velocity, Non Constant
The motion is non-constant velocity
The average velocity is the slope of the blue line joining two points

9. Instantaneous Velocity on a Graph
The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous velocity at that time
The velocity at any specific point in time
The instantaneous speed is defined as the magnitude of the instantaneous velocity

10. How would I calculate the average speed from t = 1.0s to t = 7.0s?30 20
displacement (m) 10
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Time (s)
How would I calculate the average speed from t = 1.0s to t = 7.0s?

11. Uniform Velocity Uniform velocity is constant velocity
The instantaneous velocities are always the same
All the instantaneous velocities will also equal the average velocity

12. Interpreting Motion Graphs
Area Under Curve = Displacement v t

13. How would I calculate the total displacement of this object?30 20
velocity (m/s) 10
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Time (s)
How would I calculate the total displacement of this object?

14. Interpreting Motion Graphs
Area Under Curve = Speed a t