1. Motion
Physics Unit
Physics is the scientific study of matter and energy and how they interact.
topic such as motion, light, electricity, and heat
strong rules about using numbers in math

2. Accuracy and Precision
Making measurements is an important skill in science.
Quantitative measurements give results in numbers.
Ex. A person’s temperature is 39.4 ̊C
Qualitative measurements give results in a description.
Ex. A person feels feverish
Accuracy is how good you are at using a measuring device. How close does your measurement comes to the true value.
Precision is how consistent the measuring device is.

3. Example: Golfing
4 golfers go golfing: a beginner, a consistent slice, a regular green shot, and Tiger Woods.
Tiger can hit around the hole most of the time. He has precision and accuracy.
The consistent slicer will land most shots in the same area, but probably not near the hole. They are precise, but not accurate.
The regular green shot will land most shots on the green, but not be in the same area. They are accurate, but not precise.
The beginner will probably be all over the place, on and off the green. They do not have precision or accuracy.... FORE!!

4. Questions:
Please define and give an example for each of the following:
Good Accuracy/good precision
Good accuracy/poor precision
Poor accuracy/good precision
Poor accuracy/poor precision

5. Significant Figures - A.K.A. Sig. Fig.’s
In almost every experiment, scientists measure data. These measured numbers help determine many things in life - as such, we need a way to recognize the error in each measurement.
We do this by using significant figures.
Numerically 3.0, 3.00, are of the same value, but shows that it was measured with the more precise instrument.
The zeroes in all three numbers are considered "significant figures".
They are shown to indicate the precision of the measurements.

6. Types of Numbers Exact Numbers Approximate Numbers
numbers obtained through measurement.
With these numbers we must determine how precise they are when we use them in calculations.
numbers obtained through counting.
These stand as is.

7. Determining Sig. Figs All non-zero integers are significant. Ex. 256.5
Captive zeros are always significant.
Leading zeros are NEVER significant.
Trailing zeros in a decimal are significant.
Assumed decimals are not significant. Ex
4 sig. figs Ex Ex
3 sig. figs Ex
2 sig. figs Ex
4 sig. figs
1 sig. figs

8. Rounding 3.45 10.99 When you are rounding numbers:
Consider how many sig fig.s you want to keep.
Underline that number.
Look to the number to the right of that number.
If the number after the line is 5 or more, round up.
Ex. Round to 2 sig. fig.s
= 3.5
5. If the number after the line is 4 or less, leave it alone.
Ex. Round to two sig. fig.s =
= 11
= 6.8

9. Rules For Calculations:
Multiplication and Division
Addition and Subtraction
Do the math.
The answer should contain the same number of decimal places as the number with the least decimal places.
Ex =
only one dec. place
 120.9
Do the math.
The answer should contain the same number of Sig. Figs as the number with the least number of Sig. Figs
Ex x x 12.5 =
only 2 sig. fig
 170
120.87

10. Examples: 1. 12. 58 cm + 0. 125 cm + 10. 47 cm = = 23. 18 cm 2. 25
Examples: cm cm cm = = cm m x m = 5.8 m = 57 m
23.175

11. Try These:
6.98 –
5 –
8.165 = 8.2
= 1.27
6.7548
= 2
8.88

12. Try These:
2.365 x 5.8
6.18 x 2.714
x 5.421
5 ÷
8.23 ÷ 0.65
= = = = = 13

13. Metric System Review Prefixes Metric System
Easy to use because it is based on powers of 10.
To convert from one unit to the next, you simply have to move the decimal to the left or right in the number.
When we measure the base unit can change, but the prefix stays the same.
The base units are:
Meter (m) - distance or size.
Litre (L) - volume of liquids.
Gram (g) - weight or mass.
Unit
Prefix
G -
Giga
M -
Mega
k -
Kilo
h -
Hecto
da -
Deca
m, L, or g
BASIC UNIT
d -
Deci
c -
Centi
m -
Milli
µ -
Micro
n -
Nano

14. Ketchup has destroyed my delicious chocolate milk

15. Examples 12 cm = mm 120 250 hg = kg 25 54 L = mL 54 000 3456 hm = km
345.6
109 kg = dag
10 900
0.678 g = cg
67.8 G . M K h da m d c n
Metric Mania Worksheet

16. Converting Units (Dimensional Analysis)
You can’t compare two different types of units easily
Just like you can’t directly compare quarters and dollars. They aren’t the same thing!
We have to convert units so that they are all the same in order to add, subtract, multiply, divide, or just compare them.
Conversion Factor
a ratio showing the relationship between two units
Two things that are agreed to be equal.
Ex. 4 quarters = 1 dollar or

17. Conversion Rules = 32.2 miles = 32.1875
Write the number given (with units) and a multiplication sign
Write your conversion factor
- put the unit given on the bottom
- put the unit you want to get on the top
Work out the problem.
Convert 51.5 km into miles (1.6 km = 1mile) or =
= 32.2 miles

18. Examples
Ex 1. Convert 2500 m to km *1 km = 1000 m 2500 m x 1 km = 2.5 km 1000 m Ex. 2 Convert 20 days to hours *1 day = 24 hours 20 days x 24 hours = 480 hours 1 day Ex. 3 Convert 96 hours to days *1 day = 24 hours 96 hours x 1 day = 4 days 24 hours
= 500 hours
= 4.0 days
Worksheet #1

19. Scientific Notation A number is written as the product of 2 numbers:
1) A coefficient and
2) a power of 10
Expanded Notation Scientific Notation
2305
2.305 x 103
4.58 x 10-5

20. Scientific Notation Rules:
First number (coefficient) is a number from 1-9
The first figure is always followed by a decimal point and then the rest of the digits.
Then multiply by the appropriate power of 10 (the number of times you move the decimal)
If the number you start with is big, or if you move the decimal to the left, the exponent will be positive
If the number you start with is small, or you move the decimal to the right, the exponent will be negative.

21. Standard Notation
Scientific Notation
1648
150000
7840
385000
557
1.648 x 103
1.5 x 105
6.48 x 10-4
7.84 x 103
4.8 x 10-4
3.85 x 105
5.57 x 102
4.2 x 10-4

22. Expanded Notation
If you have a positive exponent, then move the decimal to the right.
Ex x 102 =
If you have a negative exponent, then move the decimal to the left.
Ex x =

23. Try the following:
Expanded Notation
Scientific Notation
1.2 x x x x x x 102
Worksheet #3

24. Solving Equations
Depending on the variable that is wanted for a calculation, equations (or formulas) may need to be rearranged.
To rearrange an equation you must treat both sides the same.
To move a variable to the other side of the = sign, do the opposite operation (+, -, x, ÷).
If you are dividing on one side, then multiply on the other.
If you are adding on one side, then subtract on the other.

25. Example 1: D = m Solve for m
Rearrange the formula so that the m is by itself on the left hand side:
m = D

26. Example 2: D = m Solve for V
To move V: - multiply by V on both sides
D = mV
To move D: - divide by D on both sides
V = D m

27. Try the following: y = mx + b Solve for x v = d Solve for d t d = vt
x = y-b m
v = d Solve for d t
d = vt
s = r + dg Solve for r
r = s – dg
C = Rf – s Solve for f
f = C + s R
Worksheet #4

28. Section 9.5
Relating Speed to
Distance and Time

29. Speed – the distance travelled during a time interval (km/h or m/s).
Distance – the amount of space between two objects or points and is usually measured in km, or m.
Time – the duration between two events and is usually measured in s, min, or h.
Speed – the distance travelled during a time interval (km/h or m/s).
Speed =
*Vav = average speed ∆ = change in
The units of speed are:
meters/second (m/s) or kilometers/hour (km/h)
Or Vav =

30. Average Speed = 42 = = 42.0 km/hr
The total distance divided by the total time.
Ex. A person drives to work. It is 21.0 km to work, and it takes them 30 minutes. What is their average speed?
Vav =
*Remember this was their average speed.
Sometimes they drove faster and slower, and
they had to stop at signs and lights during the
trip.
= 42 =
= 42.0 km/hr

31. Instantaneous Speed
The speed of an object at a particular instant. This is often used to calculate speed for a speeding ticket, or how fast a baseball is travelling.
Two instruments for measuring instantaneous speed:
Radar guns
Speedometer

32. Constant Speed/Uniform Motion
If an object travels at the same speed for the entire trip, then it is travelling at a constant speed (setting your cruise control).
If your average speed stays the same, it will also be a constant speed, you do not speed up or slow down (cruise control).

33. Calculating Average Speed (Vav)
You may need to rearrange the formula depending whether you are looking for speed, distance, or time.
Vav =
∆d = vav ∆t
∆t = av

34. Examples Vav = = = 7.258064516 = 7.3 km/hr
Sally roller blades to school. It takes her hours to travel 4.5 km. What is her average speed?
d= 4.5 km
t = 0.62 hrs
v = ?
Vav = = =
= 7.3 km/hr

35. A nearby beach is 45 km from your house
A nearby beach is 45 km from your house. Your average speed on your bike is 20.0 km/h. How long will it take you to get to the beach?
d= 45 km
v = 20.0 km/hr
t = ?
2.25
∆t = =
= 2.3 hr

36. Bison graze at an average speed of 110. 0 m/h
Bison graze at an average speed of m/h. If these bison graze for 7 hours/day then how far will the herd travel in 14 days?
v = km/hr
t = 7 hrs a day for 14 days
d = ?
∆d = x 98hrs =
14 days x = 98 hrs
= km

37. You are travelling on a train a distance of 10. 0 km. It takes 390
You are travelling on a train a distance of km. It takes seconds. Determine the speed in km/h.
(Hint: change seconds into hours first).
d = 10.0 km
t = sec
v = ? =
390.6 sec x x =
= 92.2 km/hr
= hrs

38. Distance-Time Graph
Section 9.7

39. Graphs
Qualitative Information can’t be expressed with numbers (eg. I have a lot of tomatoes)
Descriptive properties of a substance (smell, taste, height)
Quantitative means that it can be expressed with numbers (eg. I have 24 tomatoes)
Graphs are used to represent Quantitative information visually
Easier and quicker to understand than a table or a paragraph
Help us to understand the relationship between 2 variables.
Independent Variable – The variable that is being manipulated or changed (ex. Time). This variable is found on the x-axis.
Dependent Variable – The observed result of the independent variable being changed (ex. Distance, speed). This variable is found on the y-axis.

40. Linear Graphs
Represents a direct relationship between distance and time.
Recall the equation for a straight line: y = mx + b
where: y = dependent variable (y-axis)
x = independent variable (x-axis) m = slope of the line
b = y intercept of line
Following the Speed formula becomes: d = vt + 0
d = vt
where: d = distance (y-axis)
t = time (x-axis)
v = speed (slope of the line)

41. Slope and Speed
✱ The slope of the line on a distance-time graph represents speed ✱ - The greater the speed, the greater the slope of the line of a distance time graph.

42. Try this activity:
\\Rural_310_fs\data\RURAL310\USERADM\j cacorn\Science 421\Power Points\distance_time_graphs.ppt

43. Line Graph Rules
The bigger the better. Use most of the graph paper to draw the graph. Leave large enough margins for writing.
Choose the axes. The independent variable (time) is placed on the horizontal x-axis and the dependent variable (distance) is placed on the vertical y-axis.
Choose a suitable scale for each axis. Space numbers evenly, count by 2's, 5's, 10's, etc.
Label each axis on the graph so the reader knows what the numbers represent. Include the units in brackets. Give the graph a title and a legend if necessary.
Be neat and accurate. Plot the points carefully.
Points are joined with a ruler. If the points can’t all be joined by one line draw a line of best fit. This line goes through the middle of the points touching as many as possible.

45. Calculating Speed from a Graph
the slope of the line of a distance - time graph is the average speed.
Slope = rise (change in y values) ∆d run (change in x values) ∆t

46. Slope = rise = ∆d = y2 - y1 = (50.0 m – 0.0 m)
x2 = 5.0
y1 = 0
x1 = 0
(s)
Slope = rise = ∆d = y2 - y1 = (50.0 m – 0.0 m)
run ∆t x2 - x1 (5.0 s – 0.0 s)
= 50.0 m = m/s
5.0 s

47. Slope = rise (change in y values) = (300.0 km – 0.0 km)
x2 = 5.0
y2 = 300.0
y1 = 0
x1 = 0
Slope = rise (change in y values) = (300.0 km – 0.0 km)
run (change in x values) (5.0 h – 0.0 h)
= km = 60.0
5.0 h
= 6.0 x 101 km/h

48. Graphing Activity
Using the graph below please determine the average speed during the first 2 hours, from 2 until 5 hours, and from 5 until 8 hours. Finally, calculate the average speed over the entire trip. C B A D

49. Assignment:
Read pages and do # 1, 2, 3, 5, 6 on page 365.

50. Acceleration
Section 10.3

51. Acceleration
the rate of change in speed of an object.

52. Δv a t Acceleration (a) = Δv = vf - vi t t vf is the final speed
vi is the initial speed
a = average acceleration
t = time
Δv = change in speed
Units for acceleration are always expressed as: m/s/s (meters per second per second) or m/s2 (meters per second squared) for short. OR
km/h/s (kilometers per hour per second) Δv a t

53. Refining the Acceleration Formula
In order to solve the equation for time, initial speed, or final speed you must be able to rearrange the formula:
a = vf - vi vf = vi + (at) t
t = vf - vi vi = vf - (at) a

54. Accelerating While Slowing Down
Acceleration includes a change in speed, either faster or slower. When analyzing a vehicle that is slowing down/decelerating, your acceleration will be negative.
Speeding up = + acceleration
Slowing down = - acceleration

55. Calculating Acceleration
1. A motorcycle speeds up from rest (0 m/s) to 9.0 m/s in a time of 2.0 s. What is the average acceleration?

56. 2. A car may accelerate from 0. 0 km/h to 100. 0 km/h in 6. 0 s
2. A car may accelerate from 0.0 km/h to km/h in 6.0 s. What is the average acceleration of this car?

57. 3. Kerry is moving at 1. 8 m/s near the top of a hill. 4
3. Kerry is moving at 1.8 m/s near the top of a hill s later, she is traveling at 8.3 m/s. What is her average acceleration?

58. 4. A skier accelerates at 2. 5m/s/s for 1. 5s
4. A skier accelerates at 2.5m/s/s for 1.5s. What is her change in speed at the end of 1.5s.

59. Example 1
A bus with an initial speed of 12m/s accelerates at 0.62m/s2 for 15s. What is the final speed of the bus?

60. Example 2
A skateboarder rolls down a hill and changes his speed from rest to 1.9m/s. If the average acceleration down hill is 0.40m/s/s, how long was the skateboarder on the hill?

61. Example 3
A bus with a final speed of 12m/s accelerated at 0.62m/s2 for 11s. What was the initial speed of the bus?

62. Example 1
In a race a car traveling at 100km/h comes to a stop in 5.0s. What is the average acceleration?

63. Example 2
A driver driving at 60 km/h takes 12 seconds to stop. What was her average acceleration?

64. Speed-Time Graphs for Acceleration
Section 10.4
Speed-Time Graphs for Acceleration

65. Acceleration is speed over time so to graph acceleration you must graph time on the x axis and speed on the y axis, and your slope will represent your acceleration.
Slope = Rise = ▵y = speed (y2 - y1)
Run ▵x time (x2 - x1)

66. Decreasing Acceleration
Negative speed
Slowing down
No Acceleration
Zero value
Increasing Acceleration
Positive speed
Speeding up

67. E

68. Make a Graph
Time (s)
Speed (m/s) 10 2 20 4 30 6 40 8 50

69. You can also use speed-time graphs to calculate distance
You can also use speed-time graphs to calculate distance. The distance is equal to the area under the line.
If the area under the line is a triangle, then the formula for the area is
A = ½bh where: a = area
b = base
h = height
If the area under the line is a rectangle, then the formula for area is
A = lw where: a = area
l = length
w = width

70. B A C

71. http://faraday. physics. utoronto