1. Chapter 11 Motion

2. Section 1 Objectives: Use a frame of reference to describe motion
Differentiate between Speed and Velocity
Calculate the speed of an object
Use graphs to describe speed

3. Observing Motion
Motion- an object’s change in position relative to a reference point.
Observe objects in relation to other objects that stay in place.
Meter – international unit for measuring distance.
= 50 m
1 mm

4. Frame of Reference
Frame of reference- a system for specifying the precise location of objects in space and time.
Object that you assume is fixed in place
Normally you think of walls or signs as not moving, or as being stationary objects
When you do this you use the walls or signs as a frame of reference?

5. Reference Frame
The perception of motion depends on the observer’s frame of reference
Objects is in motion when object changes position with respect to a frame of reference.

6. Describe the motion observed by one of the boys in the drawing, how does the motion appear to be different to the other boy?

7. Imagine you are the girl observing the bus, describe the motion of each object that you can see

8. What do you use as your frame of reference most of the time?

9. Displacement Displacement- the change in position of an object.
Always includes direction
Shorter than distance traveled
In the diagram:
yellow line =
distance
black arrow =
displacement

10. Measuring Motion: Speed
How do you describe motion taking place?
To describe motion you discuss speed
Speed is the distance an object travels per unit of time

11. S = d/t Calculating Speed Units for speed Ex. Cars: mi./h Jets: km/h
To calculate its speed you divide the distance it travels by the time it travels
Speed (S) = distance traveled (d) / the amount of time it took (t).
S = d/t
Units for speed
SI= m/s
Depends, but will always be a distance unit / a time unit
Ex. Cars: mi./h
Jets: km/h
Snails: cm/s
Falling objects: m/s

12. S = d/t Calculating speed
If I travel 100 kilometer in one hour then I have a speed of…
100 km/h
If I travel 1 meter in 1 second then I have a speed of….
1 m/s

13. d V t Calculating Speed Cover the one you’re looking for
Speed = Distance Time
If a runner travels 100 m in 10 seconds what was his average speed?
Probably not constant
Can solve for the other pieces too
Distance = speed x time
Time = Distance Speed d V t
Cover the one you’re looking for

14. Question
I travelled 25 km in 10 minutes. How many meters have I travelled?
A) m
B) m
C) .025 m
D) 2.5 m
25 km * 1000m/km = m

15. Practice
1. A car race is 500 km long. It takes the winner 2.5 hours to complete it. How fast was he going?
2. It is 320 km to Las Vegas. If you average 80 km/hr, how long will it take you to get there?
3. You are going on a trip. You average 80 km/hr for 6 hours. How far did you go?
V= 500km
2.5hours
V=200 km/hour
t= 320km
80 km/hr
t= 4 hours
d= (80km/hr) x 6 hrs
d= 480 km

16. Constant speed
A moving object that doesn’t change it’s speed travels at constant speed
Constant speed means equal distances are covered in an equal amount of time
Suppose you and a friend want to run around a track at constant speed for half an hour

17. Average speed Speed is usually NOT CONSTANT
Ex. Cars stop and go regularly
Runners go slower uphill than downhill
Average speed = total distance traveled total time it took

18. Calculating Average Speed
To calculate average speed figure out total distance traveled and divide by total time it took.
Problem:
It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets.
Total Distance:
40 km + 20 km = 60 km
Total Time:
1 h + 2 h = 3 hr
Ave. Speed:
total d/total t = 60 km/3 h = 20 km/h

19. Question Total Dist. = 1000 m + 1000 m = 2000 m
I ran 1000 m in 3 minutes. Then ran another 1000 m uphill in 7 minutes. What is my average speed?
A) 100 m/min
B) 2000 m/min
C) 10 m/min
D) 200 m/min
E) 20 m/min
Total Dist. = 1000 m m = 2000 m
Total Time = 3 min + 7 min = 10 min
Ave speed = total dist/total time =
2000m/10 min = 200 m/min = D

20. Velocity
An objects speed doesn’t indicate all there is to know about its motion
Velocity – the SPEED and DIRECTION of an object.
Example:
An airplane moving North at 500 mph
A missile moving towards you at 200 m/s

21. Measuring Motion: Velocity
People often use the word speed when they mean velocity
Speed tells how fast an object moves
Velocity tells both speed and direction
Object always travels in some direction
Velocity is a more precise term for describing motion
Example: Meteorologists use wind velocity measurements to help predict weather

22. Velocity Is both speed and direction. 40 km/hr = speed
40 km/hr west = velocity
Can change velocity two ways
Change speed
Change directions
Young male cheetah covered 100 meters east in 7.19 seconds in a timed run. What is his velocity?
13.9 m/s east

23. How does this graph display speed?

24. Graphing Speed: Distance vs. Time Graphs
Denver
Phoenix

25. Graphing Speed: Distance vs. Time Graphs
Speed = Slope = Rise/Run
Rise

26. Graphing Speed: Distance vs. Time Graphs
Speed = Slope = Rise/Run
Rise=?
600 km
3 h

27. Graphing Speed: Distance vs. Time Graphs
Speed = Slope = Rise/Run
Rise=?
600 m
3 minutes
Rise/Run = 600 km/3 hr
= 200 km/hr

28. Different Slopes Slope = Rise/Run = 0 km/1 hr = 0 km/hr Rise = 2 km
Run = 1 hr
Rise = 0 km
Run = 1 hr
Slope = Rise/Run
= 2 km/1 hr
= 2 km/hr
Rise = 1 km
Run = 1 hr
Slope = Rise/Run
= 1 km/1 hr
= 1 km/hr

29. Average Speed = Total distance/Total time = 12 km/6 hr
Question
Below is a distance vs. time graph of my position during a race. What was my AVERAGE speed for the entire race?
Average Speed = Total distance/Total time = 12 km/6 hr
= 2 km/hr
Rise = 12 km
Run = 6 hr

30. Why are these graphs different?
How was the motion different?

31. Question
What does the slope of a distance vs. time graph show you about the motion of an object?
It tells you the SPEED

32. Question
Below is a distance vs. time graph for 3 runners. Who is the fastest?
Leroy is the fastest. He completed the race in 3 hours

33. Motion Concepts Speed Velocity Susan 0.167 mi/m
Susan ran around the track four times for a distance of 1 mile in 6 minutes. Note: She started and stopped at the same point. Someone yelled, “Way to hustle, Susan! That’s great speed. But, your displacement is zero!” A group of friends meet at the front entrance of the mall. They spend the next 2 hours walking around the mall. One of the friends’ wrist monitors says they walked a distance of 4.2 miles. When they return to the front entrance of the mall, their displacement is zero. ** What is the difference between distance and displacement?
Speed
Velocity
Susan
0.167 mi/m
0 mi./m around the track
David
55 mph
55 mph north
Jaguar
70 mph
70 mph toward its prey
Elephant
25 mph
25 mph out of the jungle
Space-X Rocket
7.9 km/s
7.9 km/s away from earth

34. Section 2 Acceleration
Explain changes that occur when objects accelerate
Graph acceleration

35. Acceleration
Any change in velocity is acceleration, even if the speed of the object remains the same.
When ever an object changes how it moves, the velocity changes.
A change in direction is a change in velocity, and acceleration.

36. Acceleration – the rate at which velocity changes
Can be an:
Increase in speed
Decrease in speed
Change in direction

37. Types of acceleration Increasing speed
Example: Car speeds up at green light
Decreasing speed
Example: Car slows down at stop light
Changing Direction
Example: Car takes turn (can be at constant speed)
screeeeech

38. Question
How can a car be accelerating if its speed is a constant 65 km/h?
If it is changing directions it is accelerating

39. Calculating Acceleration
If an object is moving in a straight line
Units of acceleration:
m/s2
a = (Vf)-(Vi)
Time ∆V
a= ∆v t a t

40. Calculating Acceleration
a= ∆v t
Calculating Acceleration
To calculate acceleration, substrate the difference between final speed and initial speed. Then divide by time
Acceleration= Final Speed(Vf)– Initial Speed (Vi) Time
a= 16 m/s – 0 m/s 4s
a= 16 m/s 4s
a= 4 m/s2
0 s
1 s
2 s
3 s
4 s
0 m/s
4 m/s
8 m/s
12 m/s
16 m/s
Initial Speed
Final Speed

41. Question Accel= Final Speed – Initial Speed Time
A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver’s average acceleration?
Accel= Final Speed – Initial Speed
Time
= 40m/s – 20 m/s 2s
=20 m/s 2s
= 10m/s2

42. Acceleration Practice Problems
1. Natalie accelerates her skateboard along a straight path from o m/s to 4.0 m/s in 2.5 s. Find her average acceleration.
2. A turtle swimming in a straight line toward shore has a speed of 0.50 m/s After 4.0s, its speed is 0.80 m/s. What is the turtle’s average acceleration?
3. Mai’s car accelerates at an average rate of 2.6 m/s2. How long will it take her car to speed up from 24.6 m/s to 26.8 m/s?
Final speed (Vf)= 4.0 m/s
Initial speed (Vi) = 0 m/s
Time=2.5s
a = ?
a= 4.0 m/s – 0 m/s
2.5 s
a= 1.6 m/s2
Vf = 0.80 m/s
Vi = 0.50 m/s
Time= 4.0 s
a = ?
a= 0.80 m/s – 0.50 m/s
4.0 s
a= m/s2
Vf = 26.8 m/s
Vi = 24.6 m/s
Time= ?
a= 2.6 m/s2
t= ∆V a
t= 26.8 m/s – 24.6 m/s
2.6 m/s2
t= 0.85 s

43. Acceleration Practice Problems
4. Tom is driving down I-75. He notices a police officer and slows down from 81 m/s to 62 m/s in 5.0 s. Calculate his acceleration. 5. A cyclist travels at a constant velocity of 4.5 m/s westward and then speeds up with a steady acceleration of 2.3 m/s2. Calculate the cyclist’s speed after accelerating for 5.0s.
Vf = 62 m/s
Vi = 81 m/s
Time= 5.0 s
a= ?
a= 62 m/s – 81 m/s
5.0 s
a= -19 m/s
5.0 s
a= -3.8 m/s2
Vf = Vi + at
Vf = 4.5 m/s + (2.3 m/s2 x 5.0 s)
Vf = 16 m/s

44. Graphing Acceleration
Can use 2 kinds of graphs
Speed vs. time
Distance vs. time

45. Graphing Acceleration: Speed vs. Time Graphs
Speed is increasing with time = accelerating
Line is straight = acceleration is constant

46. Graphing Acceleration: Speed vs. Time Graphs
Rise = 4 m/s
Run = 2 s
In Speed vs. Time graphs:
Acceleration = Rise/Run
Find the acceleration
= 4 m/s ÷ 2 s = 2 m/s2

47. Graphing Acceleration: Distance vs. Time Graphs
On Distance vs. Time graphs a curved line means the object is accelerating.
Curved line also means your speed is increasing. Remember slope = speed.

48. Question Run = 3 s Rise = -6 m/s
Above is a graph showing the speed of a car over time.
1) How is the speed of the car changing (speeding up,
Slowing down, or staying the same)?
2) What is this car’s acceleration?
The car is slowing down
Acceleration = rise/run = -6m/s ÷3s = -2 m/s2

49. curved line = accelerating, flat line = constant speed
Question:
The black and red lines represent a objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so must be slowing down
Remember: in distance vs. time graphs:
curved line = accelerating, flat line = constant speed
Which line represents an object that is accelerating?

50. Question: Hard one
Above is a graph showing the speed of a car over time.
1)What would a distance vs. time graph for this
look like?

51. Understanding the formula
Acceleration= final velocity- starting velocity
time
Change in velocity = final – starting velocity velocity
Acceleration= change in velocity
a= ∆v t

52. Positive acceleration Positive acceleration in a negative direction