1. Science 10
Motion

2. Numbers vs. Measurement
There is a difference in between numbers used in math and measurement used in science.
In math, every number carries importance
In science, not every number in a measurement carries the same importance.
More important numbers are called significant figures.
Less important numbers are called place holders.

3. Measurement
Every measurement contains an exact amount of significant figures.
It includes all numbers that were measured from the scale used.
Plus 1 extra ‘guessed number’ that is not on the scale.
Always include one more number than your scale tells you!

4. Our scale tells us the tens and the ones so we can be certain of those numbers. We add a guessed number after the ones we are certain of.
Scale does not tell us any certain numbers, so we can only write down 1 guessed number
The scale now tells us the tens so we can be certain of those numbers. We add a guessed number after the ones we are certain of.
0 is a guessed number and it is significant
0 is a place holder and is not significant.
8 is a guessed number and it is significant
47.0 50 48
100cm
0cm
4 is a certain number and it is significant
5 is a guessed number and it is significant
47 are certain numbers and are significant

5. Rules for Significant Figures
There are 2 rules for determining the number of significant figures.
Decimal rule- (use this rule when the measurement contains a decimal)
Count the numbers from left to right beginning at the first non-zero number.

6.
6 sig. figs.
4 sig. figs.
1.234-
4 sig. figs.
5 sig. figs.
6 sig. figs.
x 10-3-
5 sig. figs.

7. Rules for Significant Figures
Non-decimal rule- (use this rule when the measurement does not contain a decimal)
Count the numbers from right to left beginning at the first non-zero number.

8. 1234-
4 sig. figs.
12340-
4 sig. figs.
5 sig. figs.
5 sig. figs.
6 sig. figs.
6 sig. figs.

9. Scientific Notation
Scientific notation is a method of writing numbers that:
Can make large numbers more easy to read.
Indicate the proper number of significant figures.

10. Rules for Writing in Scientific Notation
Write down all the significant numbers
Put a decimal after the first number. (the number will now be between 1-10)
Write “x 10”
Write the power corresponding to the number of places the decimal was (would have) been moved. (Moving right is negative, moving left is positive)
Count the number of digits between where the decimal was before and where it is now

11.
Put a decimal after the first number. (the number will now be between 1-10)
Write the power corresponding to the number of places the decimal was (would have) been moved. (Moving right is negative, moving left is positive)
Write down all the significant numbers
Write “x 10” 25 .
x 10 13

12.
Put a decimal after the first number. (the number will now be between 1-10)
Write the power corresponding to the number of places the decimal was (would have) been moved. (Moving right is negative, moving left is positive)
Write down all the significant numbers
Write “x 10”
300 .
x 10
-11

13. How do you write the number 10 000 with 3 significant figures?4
100 .
x 10

14. 123 . x 10 Change 0.00123 x 10-3 into proper scientific notation. -6
-3 -3= -6

15. Calculating using Significant Figures
There are 2 rules for calculating with significant figures.
Precision rule- (used for addition and subtraction)
The answer will have the same precision as the least precise measurement from the question.

16. 10 cm
Least precise
10. cm
10.0 cm
10.00 cm
Most precise

17. This value is the least precise value
This value is the least precise value. The answer will end at the same spot.
1.234
=1.291
Round the value after the last sig. fig.

18. This value is the least precise value
This value is the least precise value. The answer will end at the same spot.
12340 =
Round the value after the last sig. fig.
=5.690 x 106

19. Calculating using Significant Figures
Certainty rule- (used for multiplication and division)
The answer will have the same number of significant figures as the least number of significant figures from the question.

20. 123 X 45 5535 5500 3 significant figures 2 significant figures
The answer will have 2 significant figures
1 2
5500
Round the value after the last significant figure
Place holders

21. 450 X 0.0123 5.535 5.5 2 significant figures 3 significant figures
The answer will have 2 significant figures
5.5
Round the value after the last significant figure

22. Units
A unit is added to every measurement to describe the measurement.
Ex.
100 cm describes a measured length.
65 L describes a measured volume.
12.4 hours describes a measured time.
0.011 kg describes a measured mass.

23. Units In Canada we use the metric (SI) system.
The metric (SI) is a system designed to keep numbers small by converting to similar units by factors of 10.
Prefixes are added in front of a base unit to describe how many factors of 10 the unit has changed.

24. Units Base units of measurement are generally described by one lettre.
m- metre (length)
s- second (time)
g- gram (mass) *The base unit for mass is actually the kg (kilogram)
L- litre (volume)

25. Units Prefixes Prefixes are added to the front of any base unit.
Ex. mm, cm, dm, m, dam, hm, km
Kilo hecto deca base deci centi milli
(k) (h) (da) (d) (c) (m)

26. Converting units There are 2 methods to convert units
Step Method- count the number of places to move the decimal.
Dimensional Analysis- multiplication by equivalent fractions of 1.

27. Converting Units Step method-
Move the decimal the same number of spaces and direction as the distance in between prefixes.

28. Convert cm into m
Kilo hecto deca base deci centi milli
(k) (h) (da) (d) (c) (m)
We move 2 spaces to the left to get from centimetre to metre
It starts at centi (for centimetre)
So we move the decimal 2 places to the left in our number
3456 . m cm

29. 210 . 00 kg g =2.10 x 104g Convert 21.0 kg into g
Kilo hecto deca base deci centi milli
(k) (h) (da) (d) (c) (m)
We move 3 spaces to the right to get from kilogram to gram
It starts at kilo (for kilogram)
So we move the decimal 3 places to the right in our number
210 . 00 kg g
=2.10 x 104g

30. Converting Units Dimensional Analysis-
Multiply the measurement by a fraction that equals 1
The fraction will contain the old unit and the new unit.
The fraction must cancel out the old unit. (follow the rule that tops and bottoms cancel out)

31. 1 m 34.56 cm = 0.3456 m 100 cm Convert 34.56 cm into m
Kilo hecto deca base deci centi milli
(k) (h) (da) (d) (c) (m) 1 m
34.56 cm
Move 2 places so we need 2 0’s
= m
100 cm
We need to make the fraction equal 1.
Put the larger measurement as 1 and add 0’s to the smaller measurement. (# of zeroes equals the number of places the prefixes are moved.
Counted and exact values do not count for significant figures
Multiply the tops and divide the bottoms
The fraction must contain the new and old unit. Tops and bottoms cancel out
Multiply by a fraction

32. Convert kg into g
1000 g
21.0 kg
= 2.10 x104g
= 21000g 1 kg

33. Convert 15.0 m/s into km/h 1 km 60 s 60
min
15.0 m s
1000 m 1
min 1 h
= 54.0 km/h
We multiply the tops, and divide the bottoms.
We follow the same rules, but we convert 1 unit at a time.

34. 1 h 80.0 km h 1000 m 1 km 3600 s = 22.2 m/s Convert 80.0 km/h into m/s
We multiply the tops, and divide the bottoms.
We follow the same rules, but we convert 1 unit at a time.

35. Defined Equations
Relationships between variables can be expressed using words, pictures, graphs or mathematical equations.
A defined equations is a mathematical expression of the relationship between variables
Ex. Mass and Energy are related by the speed of light
E = mc2

36. Defined Equations
Defined equations can be manipulated to solve for any of the variables.
We use the same principles from math.
There are 2 rules that must be followed to isolate a variable.
It must be alone
It must be on top (numerator)

37. E = m E = mc2 c2 c2 Solve E = mc2 for m m must be isolated
Divide both sides by c2
E = m
E = mc2 c2 c2
m is already on top so we will not touch m. We have to isolate m by moving c2 to the other side.

38. v d = m v d v d Solve d = m/v for v
Multiply by v on both sides
Divide by d on both sides v d = m v d v d
v is on the bottom so we need to move v first and then isolate.

39. Speed The distance travelled by the amount of time.
How fast something is moving.
v = Δd Δt
Speed is measured in m s

40. Speed You can look at speed in 3 different ways
Average- the speed over the whole trip.
Total distance divided by total time.
Instantaneous- the speed at one point in the trip.
Looking at the speedometer.
Constant- the speed remains the same over a period of time.(uniform motion)
Cruise control.

41. Calculations for speed
Using the formula, v = d/t, we can make some mathematical calculations about speed.
Follow the same 3 steps to solve every problem.
Identify your givens and unknowns.
Identify the defined equation and isolate for the unknown variable.
Solve the equation using proper significant figures and units.

42. A trip to Calgary is 758 km. If you were to complete the trip in 7
A trip to Calgary is 758 km. If you were to complete the trip in 7.25 h, what was you speed?
Givens
Formula
Solve
d= 758 km
t= 7.25 h
v= ?
v = d t
v = 758km
7.25 h
v = 105km h

43. What type of speed did we calculate in the previous problem?
Average speed

44. If someone is travelling at a constant speed of 40
If someone is travelling at a constant speed of 40.0 km/h, how far would they travel in 32.4 min.
Givens
Formula
Solve
d= ?
t= 32.4 min
v= 40.0 km h
v = d t
d = 40.0km (0.54 h) h
d = v t
d = 21.6 km
1 h
32.4 min
= h
60 min

45. Representing Speed Graphically
We can represent speed with words (fast, slow), numbers (32 km/h) and we can also represent it visually with a graph.
Speed is represented on a distance vs. time graph.
The slope of the graph is the speed.

46. Travelled the greatest distance in the same time. (fastest speed)
Distance (m)
The slope of the line is equal to the speed
The steeper the slope, the greater the speed.
A straight line indicates a constant speed.
Travelled the least distance in the same time. (slowest speed)
A curved line indicates non-constant speed. (speeding up or slowing down.)
Time (s)

47. Describe the motion in the following graph?
1.Moving slowly at a constant speed
2.Moving faster at a constant speed
Where is the person going in this graph?
3.Not moving
4.Moving back to the start at a constant speed
5.Speeding up
Back to the original starting position.
Distance (m)
What is the speed of this graph?
0 m/s
Time (s)

48. Identify the 3 types of speed on the graph?
Average
Instantaneous
Constant
Distance (m)
the speed remains the same over a period of time
the speed over the whole trip
the speed at one point in the trip
Time (s)

49. Acceleration The change in speed by the amount of time.
How quickly something is speeding up (or slowing down)
a = Δv Δt
Acceleration is measured in m s2

50. Acceleration You can look at 2 types of acceleration.
Average- the acceleration over the whole time period.
The change in speed over time.
Constant- the acceleration remains the same over a long period of time.

51. Calculations for acceleration
Using the formula, a = Δv/Δt, we can make some mathematical calculations about acceleration.
‘Δ’ means change, Δv means change in speed
Δv = vfinal – vinitial Or
Δ v = v2 – v1

52. A person on their bike changes their speed from 10. 0 m/s to 15
A person on their bike changes their speed from 10.0 m/s to 15.0 m/s in 15.2 s. What is the acceleration of the bike?
Givens
Formula
Solve
a = 5.0m/s
15.2 s
Δ v=15.0m/s –10.0m/s
= 5.0 m/s
Δ t= 15.2 s
a= ?
a = Δv Δt
a = 0.33m s2

53. A car is traveling down the road when they see an obstruction
A car is traveling down the road when they see an obstruction. The person accelerates at -3.2 m/s2 for 5.0 s until they stop. How fast was the car moving?
Givens
Formula
Solve
v1=0 m/s –(-3.2m/s2)5.0s
v1= ?
v2= 0 m/s
Δ t= 5.0 s
a= -3.2 m/s2
a = v2- v1 Δt
v1 = 16 m/s
v1 = v2- aΔt

54. Representing Acceleration Graphically
We can represent acceleration with words (speeding up, slowing down), numbers (9.8 m/s2) and we can also represent it visually with a graph.
Acceleration is represented on a speed vs. time graph.
The slope of the graph is the acceleration.
The area under the graph represents the distance travelled

55. Increased the speed the most in the same time. (fastest acceleration)
Speed (m/s)
The slope of the line is equal to the acceleration
The steeper the slope, the greater the acceleration.
A straight line indicates a constant acceleration.
Increased the speed the least in the same time. (slowest acceleration)
A curved line indicates non-constant acceleration. (speeding up or slowing down at a changing rate.)
Time (s)

56. Describe the motion in the following graph?
1.Constantly speeding up slowly
2.Constantly speeding up faster
What is the acceleration of this graph?
3.Moving at a constant speed
4. Slowing down to a stop
A negative acceleration, they are slowing down.
speed (m/s)
What is the acceleration of this graph?
0 m/s2, but it is a constant speed.
Time (s)

57. Identify the 3 types of acceleration on the graph?
Average
Non-uniform
Constant(uniform)
speed (m/s)
the change in speed remains the same over a period of time
the change in speed over the whole trip
the speed is increasing at a changing rate
Time (s)

58. Answer the questions using the following graph.18
How long did it take for the turtle to reach 14m? 16 14
What is the average speed of the turtle over the entire trip?
distance (m) 12 10
v = d / t
v = 16.5m
78s 8
How far did the turtle get in 25s? 6
v = 0.21m s 4
It would make it about 1m
It would take 70 sec. 2 10 20 30 50 60 70 80 90
Time (s)

59. Answer the questions using the following graph.18
How long did it take for the hare to reach 10m/s?
How far did the hare travel?
A = ½ bh 16
Distance is calculated using the area under the graph
b = 80 s
H = 16 m/s
It would be travelling about 14.5 m/s 14
What is the average acceleration of the hare over the entire trip?
A = ½ (80s)(16m/s)
speed (m/s) 12
A = 640m 10
a = v / t
a = 16.5m/s
78s 8 6
a = 0.21m s2
How fast was the hare going at the 72s mark? 4
It would take 58 sec. 2 10 20 30 50 60 70 80 90
Time (s)