1. Ch. 5 A Mathematical Model of Motion
Milbank High School

2. Objectives
Study average and instantaneous velocity along with acceleration.
Use graphs and equations to solve problems involving moving objects, including free falling objects.

3. Ch. 5.1 Graphing Motion in One Dimension
Objectives
Interpret graphs of position versus time for a moving object to determine the velocity of the object
Describe in words the information presented in graphs and draw graphs from descriptions of motion
Write equations that describe the position of an object moving at constant velocity

4. Position vs. Time Graphs
It’s obvious!
Plots the position vs the time of an object.
Velocity in
this graph is
constant!

6. Is it always constant?
No!

7. Constant vs. Changing

8. Two or more objects

9. Ex. Problems Pg. 83 Pg. 84 Pg. 85 Data from a Position-Time Graph
Interpreting Position-Time Graphs
Pg. 85
Describing Motion from a Position-Time Graph

10. Uniform Motion
Means that equal displacements occur during successive equal time intervals
Pg 86, Fig 5-6

11. Determining the Slope of a Line
Pick two points on the line and determine their coordinates.
Determine the difference in y-coordinates of these two points (rise).
Determine the difference in x-coordinates of these two points (run).
Divide the difference in y-coordinates (rise) by the difference in x-coordinates (run).
Slope = rise/run.

13. What is the slope?
Rise = -24 m
Run = 8 seconds
Slope = -3 m/s

14. What is the slope?
Rise = 20s
Run = 5m
Slope = 4 m/s

15. Using Equations
While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

16. Or…….. t = any value of time d = position at that time
We can eliminate t0
Position with constant velocity
d = d0 + vt
t = any value of time
d = position at that time
d0 = position at t = 0
v = velocity
Pg. 88
Example Problem

17. Practice!
Pg. 85
Pr. 1-3
Pg. 87
Pr. 4-8
Pg. 89
Pr. 9-12

18. Sec 5.2 Graphing Velocity in One Dimension
Basically like 5.1, except velocity isn’t always constant.
Objectives
Determine, from a graph of velocity versus time, the velocity of an object at a specified time
Interpret a v-t graph to find the time at which an object has a specific velocity
Calculate the displacement of an object from the area under a v-t curve.

19. Determining Instantaneous Velocity
Draw a line tangent to the curve
The smaller the time interval, the more precise your slope is
The smaller the time ratio, the closer to the instantaneous velocity you will come

20. Velocity-Time Graphs It’s obvious! Plots the velocity vs. the time
Gives no information about the position

21. Is the velocity constant?

22. Displacement from a Velocity-Time Graph
v = ∆d/∆t
so….. ∆d = v∆t

23. Practice…
Pg. 93 Pr

24. Sec. 5.3
Acceleration
Determine from the curves on a velocity-time graph both the constant and instantaneous acceleration
Determine the sign of acceleration using a v-t graph and a motion diagram
Calculate the velocity and the displacement of an object undergoing constant acceleration

25. Which cars are accelerating??

26. Acceleration The rate of change of velocity divided by time change
Usually m/s/s…..or m/s2

27. Constant and Instantaneous Acc.
Constant-straight line on a v-t graph
Instantaneous-find the slope at a certain point on a v-t graph
Ex. Pg. 95

28. Positive and Negative Acceleration

29. Positive and Negative Acceleration
The sign of the acceleration depends upon the chosen coordinate system
Fig Pg. 96
Practice Problems….
Pg. 97 Pr

30. 5.4 Free Fall Recognize the meaning of acceleration due to gravity
Define the magnitude of the acceleration due to gravity as a positive quantity and determine the sign of the acceleration relative to the chosen coordinate system
Use the motion equations to solve problems involving freely falling objects

31. Gravity Symbol - - “g” Acceleration due to gravity= 9.80m/s2
Be aware of the signs……if upward is your positive direction, then g is going to be negative

32. Acceleration due to gravity
The acceleration of an object in free fall that results from the influence of the Earth’s gravity