1. Chapter 4
Linear Motion

2. How do we determine if an object is in motion?

3. Observing Motion Motion
An object’s change in position relative to a reference point
When an object changes position with respect to a frame of reference, the object is in motion.
north, south, east, west, up, or down

4. Group Questions Slide 1
A person sits in the passenger seat of a car that is traveling down a street. Describe the person as seen by each of the following observers:
A person sitting in the backseat of the car
A person standing on the sidewalk as the car passes
The driver of a second car moving in the same direction and passing the first car

5. Group Questions Slide 2
A person stands near a bus stop. Describe the standing person’s motion as seen by the following observers:
A person sitting in an approaching bus
A person riding in a car moving away from the bus stop
Another person standing at the bus stop

6. Discussion
Do any observers say that the person sitting in the passenger seat of the car in the first slide was moving? Explain
Do any observers say that the person sitting in the passenger seat of the car in the first slide was not moving? Explain
Do any observers say that the person standing near the bus stop in the second slide was moving? Explain
Do any observers say that the person standing near the bus stop in the second slide was not moving? Explain
Based on these answers, explain what it means when someone says an object is “moving.”

7. Observing Motion
Motion requires an object moving over a distance or how far it has moved.
When an object moves displacement takes place.

8. Distance vs Displacement
What is the difference between distance and displacement?
Which should you use when calculating how many gallons of gas you will need for a road trip?
Which does the saying “as the crow flies” refer to?

9. Speed Speed tells you how fast something traveled over specific time.
Speed is calculated as distance d divided by time t.
s=d/t
Speed can also be measure in small spurts called instantaneous speed.
Ex. Speedometer in a car

10. Problem Situation
I have dinner reservations at 8 pm at the Spaghetti Warehouse in Marietta off of exit I just got on I-75 South from Barrett Parkway at exit Assuming the distance from here to there is 10 miles, and it is now 7:50 pm, how fast must I drive to make my reservation?
I know that Speed equals distance divided by time
Distance is 10 miles
Time is 10 minutes
Speed = distance = miles = 1 mile / minute!
time minutes

11. Total Distance Covered
Helpful Hint
Average Speed = total distance covered
travel time
Total Distance Covered D S T
Average Speed
Total Time

12. Velocity
Velocity not only tells you the speed of an object but it also tells the direction.
When velocity is calculated you use the same equation as speed, but you must specify direction.

13. Problem
It takes you 60 mins to travel 2km, what is your average speed?

14. Graphing Motion A graph can be used to study motion
Distance – Time graph
x-axis= time
y-axis= distance
The slope of the line is the speed

15. Practice
Make a line graph of the data of a runner. Determine the during which time interval the runner is moving faster, moving slower, and standing still. Explain the relationship between the slope of the line and the runner’s speed.
Time (s)
Position (m) 10 20 30

16. Answer

17. Motion Diagram

18. 6 m
5 m
4 m
3 m
2 m
1 m
Distance
3 s
2.5 s
2 s
1.5 s
1 s
.5 s
Time
Position versus Time 7
Position
(meters) 5 3 1 1 2 3
Time - (seconds)

19. Question?
Which line shows the object covering the most ground in a certain amount of time?
Position versus Time
Position
End of Lecture was here
Time

20. Some Names??
We call the distance an object travels in a certain amount of time “speed”
Speed = Distance covered
Time
Two Types of
Instantaneous
Average

21. Distance over Time is ? Distance versus Time 7 Distance (meters) 5 1 2
Time - (seconds) 1 2 3
Distance versus Time 5 7
Distance divided by time on this kind of graph is the:
___________ of the object
___________ of the line

22. Question?
Which line shows the object covering the most ground in a certain amount of time?
Position versus Time
Position
Time

23. Question?
Which object has the highest rate of speed or rather, which object is moving the fastest?
Position versus Time
Position
Time

24. Question? Rank the five colors in order from slowest to fastest.
Position versus Time
Position
Time

25. Changes Velocity is Speed + Direction How can we change our speed?
How can we change our velocity?

26. Acceleration Whenever your speed or direction changes you accelerate.
Calculate acceleration
a= vf-vi/t

27. Think about it
Think about your daily life. List 5 examples of acceleration. Classify each example of acceleration as an increase in speed, a decrease in speed, a change in direction, or a combination.

28. Is your friend right?
Your friend Lynn is getting frustrated that y’all are driving in circles [literally] trying to find the store. Lynn looks at the speedometer, sees its not moving from 25 mph and says: “Well, at least we are not accelerating while driving around the around the mall.” What do you say to Lynn?

29. Revisit Motion Diagrams
Spacing between dots represent what?
Arrows represent what two things?
If the object started to move faster towards the left, what would the diagram look like now?

30. Check your representation skills!
Construct a motion diagram for the ball in this video!
Video

31. Discuss with neighbor
Which diagram below resembles your diagram the most? C D A B

32. Discuss with neighbor
In what direction is your CHANGE in velocity for that video/motion diagram? C A B
Change in velocity is zero

33. Discuss with neighbor
In what direction is your CHANGE in velocity for that video/motion diagram? C A B
Change in velocity is zero

34. Motion Diagram
Combine the two and you get: Dv

35. Create a story
Devise a story for an object whose motion is consistent with the motion diagram. Dv
Dv = 0 Dv

36. Create a story Dv
Devise a story for an object whose motion is consistent with the motion diagram to the right. Dv
Dv = 0

37. Throw the ball up now?
We just did a motion diagram for a ball on its way down.
Imagine, if I throw the ball up in the air? What does a motion diagram look like for the ball while it is moving upwards?
While its at the top?

38. Example Problem
I am standing on a cliff and I drop a rock from rest. After two seconds, the rock is moving at a speed of 20 m/s. What is the rate of acceleration for this rock?
I know that acceleration equals change in velocity per unit time
Change in Velocity is 20 m/s
Time is 2 seconds
Acceleration = D velocity = m/s = m/s/s or
time s 10 m/s2

39. Question
If I can accelerate at a rate of 15 mph per second, how long will it take me to accelerate from 30 to 90 miles per hour?

40. Question
If I can accelerate at a rate of 15 mph per second, how long will it take me to accelerate from 30 to 90 miles per hour?
2 seconds
4 seconds
8 seconds
900 seconds

41. Question
You are in your car going 75 mph. If you can decelerate your car at a rate of 25 mph per second, then how long does it take you to stop your car?

42. Question
You are in your car going 75 mph. If you can decelerate your car at a rate of 25 mph per second, then how long does it take you to stop your car?
100 seconds
1/3 second
3 seconds
50 seconds
What is the direction of the objects acceleration compared to the velocity of the car?

43. Problem
A flowerpot falls off a second-story windowsill. The flowerpot starts from rest and hits the sidewalk 1.5s later with a velocity of 14.7m/s. Find the average acceleration of the flowerpot.

44. Mathematical Representations learned thus far
v = Dd / Dt = velocity equals change in displacement over change in time
a = Dv / Dt = acceleration equals change in velocity over change in time
Free Fall Only Starting at Rest!!!!!!!
a = g = 10 m/s2 [actually 9.8 m/s2]
v = g t = velocity is g multiplied by time
d = ½ g t2 = distance is one half multiplied by g multiplied by times squared.