1. Tues. Feb. 18 Do NOW
What is the difference between an independent variable and a dependent variable? Give an example of each. Do lab activity with CPO timers and photogates.

2. Wednesday, Feb. 19 DO NOW
What metric (SI) units do we use to describe: 1- distance 2- time 3- mass 4- speed

3. The / sign means divided by or per.
Speed
Speed is the rate at which an object
moves across a distance per unit of time.
Speed = Distance /Time
The / sign means divided by or per.
The units in which speed is measured include any units of length or distance divided by any unit of time.

4. Units of speed
Examples of units of speed include: -miles/hour -meters/second -feet/second -kilometers/hour Your textbook will usually use the units of meters per second (m/s) for speed.

5. If you ride a bike a distance of 5 meters in 1 second, what is your speed? If you ride a bike a distance of 10 meters in 2 seconds, what is your speed? If you ride a bike a distance of 100 meters in 20 seconds, what is your speed?

6. Instantaneous Speed- The speed at a given instant in time
Instantaneous Speed- The speed at a given instant in time. Example: You are driving down the road. Your speedometer reads 25 mph. 25 mph is your instantaneous speed. The speed you see on a car speedometer is an instantaneous speed.

7. Average Speed
Average speed – total distance covered/time interval Average speed does not tell you anything about your maximum or minimum speed. Example: If you travel 240 km in 4 hours, your average speed is 240 km/4 hr = 60 km/hr

8. You are driving 200 km to a concert in Madison
You are driving 200 km to a concert in Madison. At one point you look at your speedometer and see that it reads 100 km/hr. You arrive at the concert in 2 hours. -What was your average speed? -What was your instantaneous speed at one point on your trip?

9. Speed vs. Velocity
Speed is a description of how fast an object moves. Velocity is a description of how fast and in what direction an object moves. Velocity is speed with direction.

10. Examples of Velocity Measurements: -50 km/hr north -20 ft/s left -45 m/s southeast (SE) Does a car speedometer read speed or velocity? How do you know?

11. Constant Velocity Constant velocity requires constant speed AND constant direction. If an object is moving in a circular path at a constant speed, it is NOT moving with constant velocity because its direction is changing.

12. An object whose direction or speed is changing is moving with a changing velocity. Homework: Read Sec. 2.2 & 2.3 pg Do problems 2-8 on page 25 and problem 26 on page 26

13. Thurs. Feb. 20 DO NOW
Is the movement described below constant or changing velocity? 1-a child riding on a Ferris wheel at a constant speed; 2-a car driven at constant speed down Silver Spring Rd; 3-a student walking down stairs at a constant speed; 4-birds flying south for the winter; 5-Ms. Bandoian as she walks around the classroom?

14. Acceleration – the rate at which velocity is changing over time
Acceleration = change in velocity
time interval

15. Acceleration is the rate at which velocity (speed) changes.
If your speed increases by 1 m/s each second, then your acceleration is 1 m/s per second.
What is the acceleration for the steeper hill?

16. Speed and acceleration
Speed and acceleration are not the same thing. Acceleration is the change in speed divided by the change in time.

18. Solving Problems
A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 s. Calculate acceleration.

19. Solving Problems
Looking for: acceleration of sailboat
Given:
vstart =1 m/s; vfinish = 4 m/s; time =3 s
Relationships:
a = vfinish – vstart/t
Solution:
a = (4 m/s – 1 m/s)/ 3 s
= 1 m/s2

20. Speed and acceleration
An acceleration in m/s/s is often written as m/s2 (meters per second squared). It is better to think about acceleration in units of speed change per second (that is, meters per second per second).

21. Acceleration is positive when velocity is increasing, for example when a car is speeding up.
Acceleration is negative when velocity is decreasing, for example when a car is slowing down. Negative acceleration is called deceleration.

22. Acceleration can be happening even if the speed of an object is not changing.
Remember, velocity consists of speed and direction. If the direction of motion is changing but the speed remains the same, the object is accelerating.

23. Acceleration and Direction
Acceleration occurs whenever there is a change in speed, direction, or both.

24. Practice Problem:
As a shuttle bus comes to a normal stop, it slows from 9.00m/s to 0.00m/s in 5.00s. Find the average acceleration of the bus.

25. Practice:
a) A ball is dropped off a bridge
Accelerating? Yes No
Speed? Increase / Decrease / Neither
b) A man is running at a constant speed

26. Homework:
Read pg
Pg. 25 Review Questions 9-11
Pg. 26 Probs. 27, 28

27. Fri. feb. 21 DO NOW
Write the formula for acceleration.
Rearrange the formula so that t is the subject:
d = ½ gt2

28. Reaction time activity

29. Monday, Feb. 24 DO NOW 3- Centi- means _________.
1-Describe a situation when acceleration is positive.
2-Describe a situation when acceleration is negative.
3- Centi- means _________.
4- One meter = _____ centimeters
5- One centimeter = ___ millimeters
6- A millimeter is what fraction of a centimeter?
____________
7- One kilometer = _____meters
8- Kilo- means _________.

30. Review of speed, velocity, & acceleration
Instantaneous Speed = speed at a given instant Average Speed = the total distance traveled divided by the total time of travel

31. Velocity is speed with direction.
Speed is a description of how fast an object moves.
Velocity is a description of how fast and in what direction an object moves.
Velocity is speed with direction.
Constant velocity requires constant speed AND constant direction.
If an object is moving in a circular path at a constant speed, it is NOT moving with constant velocity because its direction is changing.

32. Acceleration – the rate at which velocity is changing over time
Acceleration = change in velocity
time interval

33. It is often useful to look at data on graphs.
This is true of data on velocity and acceleration so we will do a review of graphing.

34. Line Graph
A line graph is a graph that uses line segments to connect data points and show changes in data.

35. 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 variables cause changes in the other variable.
Graphs help us see a cause & effect relationship.

36. The position vs. time graph
To graph data, you put position on the vertical (y) axis
Dependent variable
Time goes on the horizontal (x) axis.
Independent variable

37. The position vs. time graph
An object moving at a constant speed always creates a position vs. time graph that is a straight line.

38. Slope
You can use position vs. time graphs to quickly compare the speeds of different objects.
A steeper line on a position vs. time graph means a faster speed.

39. Slope
The “steepness” of a line is called its slope.
The rise is equal to the height of the triangle.
Change in Y-axis value
The run is equal to the length along the base of the triangle.
Change in X-axis value

40. The slope is equal to the rise divided by the run.
The slope for position vs. time graph is therefore distance (position) divided by time.
Which equals WHAT?
Slope

41. Practice:
How far did runner B travel in 100 seconds?
How far did runner A travel in 100 seconds?
Who was traveling at a faster speed?

42. Practice Continued:
Calculate the average speed of runner A (total distance ÷ total time)
Calculate the average speed of runner B (total distance ÷ total time)

43. *
07/16/96
Graphing Motion
slope = steeper slope = Straight line = flat line = Single point = instantaneous speed
speed A B
faster speed
constant speed
no motion *

44. Who had a constant speed? A Describe B from 10-20 min.
Graphing Motion
Who started out faster?
A (steeper slope)
Who had a constant speed? A
Describe B from min.
B stopped moving
Find their average speeds.
A = (2400m) ÷ (30min) A = 80 m/min
B = (1200m) ÷ (30min) B = 40 m/min A B

45. Do practice problems on your note sheet
Do practice problems on your note sheet. Any not completed in class are homework!

46. Tues. Feb. 25 DO NOW
Use a ruler to graph the following points on a sheet of paper from the wire tray on the front table. x y Draw a line between the points.

47. *
07/16/96
Graphing Motion
slope = steeper slope = Straight line = flat line = Single point = instantaneous speed
speed A B
faster speed
constant speed
no motion *

48. Who had a constant speed? A Describe B from 10-20 min.
Graphing Motion
Who started out faster?
A (steeper slope)
Who had a constant speed? A
Describe B from min.
B stopped moving
Find their average speeds.
A = (2400m) ÷ (30min) A = 80 m/min
B = (1200m) ÷ (30min) B = 40 m/min A B

49. Four steps to make a graph
Step 1: Choose which will be the dependent and independent variables. The dependent variable goes on the y-axis and the independent variable goes on the x-axis.

50. Four steps to make a graph
Step 2: Make a scale for each axis by counting boxes to fit your largest value. Count by multiples of 1, 2, 5, or 10. Scale must be consistent – if one line on the x-axis is equal to 1 hr the rest of the lines on the x-axis must be equal to 1 hr.

51. To determine scale, first you must determine the range of your data
Step 2 Continued
To determine scale, first you must determine the range of your data
Range is equal to your highest data value
Ex:
If the range of your data is 0-23 your scale could be counting by 5s up to 25.

52. Four steps to make a graph
Step 3: Plot each point by finding the x-value and drawing a line upward until you get to the right y-value.

53. Four steps to make a graph
Step 4: Draw a smooth curve that shows the pattern of the points. Do not just connect the dots.

54. Data

55. Four steps to make a graph
Step 1: Choose which will be the dependent and independent variables. The dependent variable goes on the y-axis and the independent variable goes on the x-axis. In the example which of the variables (time or distance) depends on the other? Dependent variable = Independent variable =
Distance
Time

56. Four steps to make a graph
Step 2: Make a scale for each axis by counting boxes to fit your largest value. Count by multiples of 1, 2, 5, or 10. Scale for distance: 1 line = Range = Scale for time: 1 line =
10 km 60
1 hour 6

57. Distance (km) Time (hr) Step 3: Plot Points 0 10 20 30 40 50 60
Distance (km)
Time (hr)

58. Step 4:Graph
Distance (km)
Time (hr)

59. get some graph paper from the metal tray on the front table
get some graph paper from the metal tray on the front table. do the practice problems on your note sheet. Any not finished by the end of class are homework!

60. Wed. feb. 26 do now
A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the helicopter’s acceleration? A skateboarder traveling at 9.0 m/s rolls to a stop at the top of a ramp in 3.0 seconds. What is the acceleration of the skateboarder? A race car accelerates from 18 m/s to 32 m/s in 2 seconds. Determine the acceleration of the car.

61. steeper slope = faster speed straight line = constant speed*
07/16/96
we have learned to analyze and make distance vs. time graphs. We saw that: A B
slope = speed
steeper slope = faster speed
straight line = constant speed
flat line = zero speed
single point = instantaneous speed *

62. Now we will look at Speed vs. Time Graphs

63. Acceleration and Motion Graphs
A speed vs. time graph is useful for showing how the speed of a moving object changes over time.
If the line on the graph is horizontal, then the car is moving at a constant speed.
There is no change in speed so there is no acceleration.

64. Slope
You can use speed vs. time graphs to determine acceleration Remember: The “steepness” of a line is called its slope.
Speed vs. Time

65. Slope
-The slope is equal to the rise divided by the run -The slope for speed vs. time graph is therefore change in speed divided by time, which equals WHAT? ACCELERATION
Slope = rise
run
Slope = change in v change in t
Slope = 8-4 = 2 m s2
Speed vs. Time

66. Acceleration and Motion Graphs
Positive acceleration adds more speed each second.
Positive slope: the line slopes upwards

67. Acceleration and Motion Graphs
Negative acceleration subtracts some speed each second, so things get slower.
Negative slope: the line slopes downwards
Speed is decreasing at the same rate.

68. Acceleration and Motion Graphs
The position vs. time graph also shows acceleration.
This graph is a curve when there is acceleration.

69. Review of terms: Distance: amount of space between 2 points
Speed: how quickly something moves over a distance; distance divided by time
Velocity: the same as speed but with a specific direction.
Acceleration: the rate at which speed or velocity changes; change in speed divided by time

70. Reading Graphs: Position vs. Time
x-axis (independent variable): Time
y-axis (dependent variable): Position
Slope = speed
Horizontal line: at rest; speed is zero
Straight line: constant speed; speed not changing
positive slope = moving away from starting point
negative slope = moving toward starting point
Curved line: changing speed (acceleration)
Speeding up or slowing down

71. Reading Graphs: Speed vs. Time
x-axis (independent variable): time
y-axis (dependent variable): speed
Slope = Acceleration
Horizontal line = constant speed; zero acceleration
Straight line = constant acceleration (speed is changing at the same rate every second)
positive slope = acceleration increasing
negative slope = acceleration decreasing (deceleration)

72. Thur. Feb. 27 do now
In the position vs. time graph what is graphed on the y-axis?
On the x-axis?
What is the independent variable?
Dependent variable

73. Speed, Distance, and Time Quiz