1. Describing Motion

2. Some Physics Quantities
Vector - quantity with both magnitude (size or numerical
value) and direction
Scalar - quantity with magnitude (size or numerical
value) only
Vectors:
Displacement
Velocity
Acceleration
Momentum
Force
Scalars:
Distance
Speed
Time
Mass
Energy

3. Vectors Often represented by arrows.
Length of the arrow represents the magnitude (how far, how fast, how strong, etc. depending on the type of vector)

4. Do you know the difference?
Quantity
Category
5 m
30 m/sec, East
5 mi., North
20 degrees Celsius
256 bytes
4000 Calories
Scalar
Vector
Vector
Scalar
Scalar
Scalar

5. Kinematics
The study of motion of an object without regard to the causes of the motion.

6. Reference Frame
1 minute!!! Discuss with the person next to you: Is the speed of the ball different relative to the pitcher, the truck driver, and the jet pilot? Why or why not?

7. Reference Point and Position
To locate an object we need a reference point
Reference Point – the origin – the starting point you choose to describe the position of an object.
We also then need to consider where the object is relative to the origin – the position of the object.
Position (x) – where you are located
A complete description of position includes:
Distance
Direction
Reference Point

8. Position
The object’s position is its location with respect to a chosen reference point.
Consider the point to be the origin of a coordinate system.
In the diagram, allow the road sign to be the reference point.

9. Distance Distance (d) – how far an object travels.
Does not depend on direction.
Scalar or vector quantity?
Imagine an ant crawling along a ruler.
What distance did the ant travel?
Scalar cm 1 2 3 4 5 6 7 8 9 10
d = 3 cm

10. Distance Distance does not depend on direction.
Here’s our intrepid ant explorer again.
Now what distance did the ant travel?
d = 3 cm
Does his direction change the answer? cm 1 2 3 4 5 6 7 8 9 10

11. Distance Distance does not depend on direction.
Let’s follow the ant again.
What distance did the ant walk this time?
d = 7 cm cm 1 2 3 4 5 6 7 8 9 10

12. Displacement
Displacement (x) – where you are in relation to where you started.
Does depend on direction. Vector Quantity
Displacement = final position – initial position
Examples of directions:
+ and –
N, S, E, W
Angles

13. Displacement
Let’s revisit our ant, and this time we’ll find his displacement.
Distance: 3 cm
Displacement: +3 cm
The positive gives the ant a direction! cm 1 2 3 4 5 6 7 8 9 10 + -

14. Displacement Find the ant’s displacement again. - + Distance: 3 cm
Remember, displacement has direction!
Distance: 3 cm
Displacement: -3 cm cm 1 2 3 4 5 6 7 8 9 10 + -

15. Displacement Find the distance and displacement of the ant. - +
Distance: 7 cm
Displacement: +3 cm cm 1 2 3 4 5 6 7 8 9 10 + -

16. Displacement vs. Distance
Example of distance:
The ant walked 3 cm.
Example of displacement:
The ant walked 3 cm EAST.
An object’s distance traveled and its displacement aren’t always the same!

17. Distance vs. Displacement
You drive the path, and your odometer goes up by 8 miles (your distance).
Your displacement is the shorter directed distance from start to stop (green arrow).
start
stop

18. Motion in Dimensions 1 dimension 2 dimension
Distance/length is measured in ONE direction (left to right OR north to south)
2 dimension
Distance/length is measured in TWO dimensions (north and east OR south and west)

19. Practice Problem 1
An athlete runs around a track that is 100 meters long three times, then stops.
What is the athlete’s distance and displacement?
Distance = 300 m
Displacement = 0 m
Why?

20. Practice Problem 2
A whale swims due east (from 0km) a distance of 5km, turns around and goes due west for 2km and finally turns around again and heads 4km due east.
What is the total distance traveled?
What is the displacement?

21. Practice Problem 3 Motion Distance Traveled Displacement X
An object moves from point 1 to point 4 then reverses and ends at point 2
An object moves from point 1 to point 5 then reverses to point 2
An object moves from point 1 to point 3 then reverses to 0
An object moves from point 3 to point 5 and then reverses to point 1
An object moves from point 2 to point 4 and reverses to point 2

22. Practice Problem 4
Janice drives her scooter 7 kilometres north. She stops for lunch and then drives 5 kilometres east. What distance did she cover? What was her displacement?

23. Practice Problem 5
David walks 3 km north, then turns and walks 4 km east. Express your answer in kilometers

24. Practice Problem 5 Answer Key

25. Electric Current Notes
Rates
A rate measures how fast something changes.
In physics, a rate is almost always calculated as a quantity divided by time.
Speed, Velocity and Acceleration

26. Speed Speed (s) – Rate at which an object moves
speed = distance / time
s = d/t
Units: m/s OR km/h
Like distance, speed does not depend on direction.
Scalar or Vector?
Scalar

27. Types of Speed
Constant speed - Speed that does not change (same distance is travelled the same amount of time)
Instantaneous speed – Speed at a given instant in time (what the speedometer says)

28. When completing a formula you MUST show all your work!
Step 1 – write formula
Step 2 – plug in the information you are given
Step 3 – solve
Step 4 – add your units (and direction if needed)

29. Practice A car drives 100 meters in 5 seconds.
What is the car’s speed?
s = d/t
s = (100 m) / (5 s) = 20 m/s
100 m
5 s
4 s
1 s
2 s
3 s

30. Practice
A hydroplane boat, made speed records by traveling 239 miles in 0.75 hours (45 minutes). What is it’s record breaking speed?
d/t miles/ 0.75 hr

31. Average Speed
Average speed - Total distance traveled divided by total time traveled.

32. Practice Problem: Average Speed
Melissa shot a model rocket 360 m into the air. It took the rocket 4s to fly that far. What was the average speed of the rocket?

33. Practice Problem: Average Speed
If Jessica ran 5 meters the first second, eight meters the next second, and 8 meters the third second to her house. What was her average speed?

34. Speed: Average vs. Instantaneous

35. Can I determine time given distance and speed? How?
A rocket is traveling at 10 km/s. How long does it take the rocket to travel 30 km?

36. Can I determine distance given time and speed? How?
A racecar is traveling at 85.0 m/s. How far does the car travel in 30.0 s?

37. Calculating Speed, Distance or Time
If you know any two of the variables, you can calculate the missing variable.

39. Is their speed the same? Is their velocity the same?

40. Velocity Velocity (v) – measure of speed in a given direction.
velocity = x / time, w/ direction
Scalar or Vector?
The velocity of an object can change if:
Vector
It speeds up
It slows down
It changes direction

41. Velocity Practice
What is the velocity of a car that traveled a total of 75 kilometers in 1.5 hours from Florida to New Jersey?

42. Speed Vs Velocity
An object is moving in a circle at a constant speed of 10 m s-1.
We say that it has a constant speed but its velocity is changing. Why?
Direction of Motion
The direction of the object keeps changing.

43. Average Velocity Displacement in a given amount of time.
Average Velocity = total displacement
total time

44. Average Velocity Practice
A man walks 7km in 2 hours West and 2 km in 1 hour back toward the East.
What is the man’s average velocity?
What is the man’s average speed?

45. Average Speed and Velocity Practice
A teacher walks back and forth in front of the room during a lesson. She starts at one end of the desk and walks from the door to the windows, a distance of 4.0m in 5 s. She then stops, turn around and walks 2.0 m back toward the door in 3 s. She stops here for 10 s and then walks 3 meters toward the door in 6 s.
What is the average speed of the teacher?
What was the average velocity of the teacher?

46. Average Velocity Practice
You drive your truck south for 5.2 miles in 10 minutes, at which point you run out of fuel. You walk 1.2 miles further to the nearest gas station in 30 minutes. What is your average velocity?

47. Pulling It All Together
Back to our ant explorer!
Distance traveled: 7 cm
Displacement: +3 cm
Average speed: (7 cm) / (5 s) = 1.4 cm/s
Average velocity: (+3 cm) / (5 s) = +0.6 cm/s cm 1 2 3 4 5 6 7 8 9 10 + -
5 s
4 s
1 s
2 s
3 s

48. Distance vs. Time Graph Important Graphing Information
1. Draw your axes
2. Label your axes
3. Choose your intervals
4. Choose appropriate spacing between intervals.
5. Plot your data
6. Draw a line best fit
7. Give your graph a title

49. Graphs show relationships
A good way to show a relationship between two variables is to use a graph.
A graph makes it easy to see if changes in one variable cause changes in the other variable (the effect).
Distance
Distance

50. The distance vs. time graph
To graph data, you put time on the horizontal (x) axis – this is your independent variable.
Distance goes on the vertical (y) axis – this is your dependent variable.
Distance
Distance

51. The distance vs. time graph
Distance vs. time data tells you the runner’s position at different points in time.
The runner is at 50 meters after 10 sec., 100 meters after 20 sec. and 150 meters at 30 sec.
Distance
Distance

52. A straight, diagonal line indicates…
Constant Speed
Why is the line in a constant speed graph straight and diagonal?
The object is traveling the same distance in the same amount of time.

53. An Object At Rest Object’s AT REST are not moving
A horizontal line on a Distance vs. Time graph has NO SLOPE = 0 speed

54. object is not moving,
constant speed
negative velocity (reversing or moving in the opposite direction.)

55. A curved line indicates…
Changing Speed

56. Distance-Time Graph and Changing Speed
What do the different lines indicate when an object is changing speed?
Downward Curve
Horizontal Line
Upward Curve
Slowing down
Stopping
Speeding Up

57. Comparing Slopes Fast, steady speed Increase speed stationary
Constant speed
stationary
Change direction at a constant rate

58. Terry, Jade and Jerome Raced. Plot their data on a distance vs
Terry, Jade and Jerome Raced. Plot their data on a distance vs. time graph

60. How to determine total average speed by looking at a line graph
Find total distance (ending distance)
2. Divide by total time (ending time) t t

61. Comparing speeds on a Distance – Time Graph
1. Find the average speed of each line.
2. Compare the steepness
of each line.
The steeper slope indicates:
Faster Speeds

62. Distance vs. Time Graphs
Which graph shows the faster moving object?

63. What does the slope tell you on a distance vs. time graph?
Rise =
Run =
Rise/Run =
Distance (y axis)
Time (x axis)
Speed or velocity

64. Graphing Speed Distance vs. Time Graph
Slope:
Rise/Run (y2-y1) / (x2-x1)

65. Graphing Speed Distance vs. Time Graph Slope

66. Graphing Speed Distance vs. Time Graph Slope

67. Practicing with Slope

68. Practicing with Slope

69. Practicing with Slope
We can now quantify the results because we have gridlines, numbers and aces.
Calculate the slope from A to B
Slope = rise/run

70. Practicing with Slope
Calculate slope from B to C

71. Practicing with Slope Calculate slope from C to D
Practice problem is from

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

73. Types of acceleration Increasing speed Decreasing 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

74. Calculating Acceleration
Units of acceleration:
m/s2

75. A bicyclist started from rest along a straight path
A bicyclist started from rest along a straight path. After 5s, his speed was 8m/s. What was his acceleration during the time?

76. Can we find time?
A car accelerates at a rate of 3.0 m/s2. If its original speed is 8.0 m/s, how many seconds will it take the car to reach a final speed of 25.0 m/s?

77. Can we find Final Velocity?
A motorcycle traveling at 25m/s accelerates at a rate of 7.0m/s2 for 6.0 seconds What is the final speed of the motorcycle?

78. Graphing Acceleration Speed – Time Graphs
Shows how changes over time
X axis =
Y axis =
SPEED
TIME
SPEED

79. Object at Rest The speed is zero and does not change
Horizontal line (like a
distance – time graph y = 0 )

80. Constant Speed The line will be HORIZONTAL
The further the line is from the
the
It is moving.
X - AXIS
FASTER SPEED

81. Speeding Up CLOSER BEGINNING LOWER UPWARD INCREASES
The line on a speed – time graph is
to the x-axis in the of the
time period when it has a speed.
CLOSER
BEGINNING
LOWER
The line slants toward the
right side of the graph as the
speed
UPWARD
INCREASES

82. Slowing Down FAR DECREASES CLOSER DOWNWARD ZERO
When initially starting to slow down the
point representing speed is
from the x-axis.
FAR
As speed the points
representing speed get
to the x-axis.
DECREASES
CLOSER
The line on a speed-time graph slopes
to the right.
DOWNWARD
When the line touches the x-axis, the speed is and the object
stopped.
ZERO

86. Comparing Distance – Time and Speed – Time Graphs
Objects at Rest

87. Comparing Distance – Time and Speed – Time Graphs
Constant Speed

88. Comparing Distance – Time and Speed – Time Graphs
Speeding Up

89. Comparing Distance – Time and Speed – Time Graphs
Slowing Down