1. Non-Constant Velocity
Motion with
Non-Constant Velocity

2. How can we describe the motion of our car traveling down a ramp?
What trends do you notice?

3. Analysis of Position-vs-Time Graph
Object’s velocity is increasing, evidenced by a larger change in position during later time intervals
For an object that do not travel at constant velocity, the slope of its position-vs-time graph is not constant

4. Average Velocity: Graphically
The slope of a line connecting two points represents the average velocity of the object between two moments in time.

5. Instantaneous Velocity: Graphically
The slope of the tangent line represents the instantaneous velocity of the object at any one instant in time

6. Velocity vs Time Graphs
The vertical axis represents the object’s velocity as a function of time.

7. Interpreting v-t graphs
Describe what each of the following v-t graphs represents about the moving object.
(a)
(b)
(c)

8. Find the Mathematical Function for this graph 6 5 4 3 2 1 v0
a is acceleration
vi is the initial velocity

9. Acceleration
Acceleration (a) – a vector that represents the rate of change of an objects’ velocity
Acceleration only occurs if its velocity is changing:
Speeding up
Slowing down
Changing direction

10. Acceleration
Equation: Units:
Same as slope on a v-t graph!

11. What would be the displacement of the object in the 8 seconds? 6 5 4 3 2 1
Average Velocity

12. What are we really finding about the graph when we find displacement
What are we really finding about the graph when we find displacement? (Think geometry) 6 5 4 3 2 1
8 s
4 m/s
Area!

13. What would be the displacement of the object in the 8 seconds? 6 5 4 3 2 1

14. What are we really finding about the graph when we find displacement
What are we really finding about the graph when we find displacement? (Think geometry) 6 5 4 3 2 1
8 s c
Area!
4 m/s

15. How would you find the displacement?
3m/s
Positive Area!
6 s
Negative Area!
12 s
-3m/s

16. Displacement from a v-t graph
Displacement is the area under a velocity vs. time graph
Area is positive above t-axis
Area is negative below t-axis

17. Making Connections .

18. Making Connections

19. Making Connections

20. Motion Quiz Vectors vs. Scalars Distance vs. Displacement
Speed vs. Velocity
Interpreting Distance vs Time graphs:
Find displacement over a certain time
Find velocity at a certain time
Average velocity for trip
What variable represents the slope of a line
Interpreting Velocity vs Time graphs
Velocity at a certain time
Acceleration at a certain time
Displacement over a certain time