Unit 1 : Kinematics 2204 unit 1...Distance VS Displacement Distance : total ground covered travelling from A to B For example: Walking forward 3 km, then back 4 km gives a distance

Physics 2204 Unit 1.notebook

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Unit 1 : Kinematics


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Scalars

• 5 km

• 15 minutes

• 110 km/hr

Vectors

• 3 km [left]

• 9.8 m/s2 [down]

• 14 m/s [east]

Scalars and Vectors

From 1206:

• Scalars have only magnitude (and units)

• Vectors have magnitude and direction / bearing (and units)


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Distance VS Displacement

Distance : total ground covered travelling from A to B

For example: Walking forward 3 km, then back 4 km gives a distance of 7 kilometers.

(As a side note, the standard unit of distance is meters)

Displacement: the shortest path from A to B

For example: Walking forward 3 km, then back 4 km gives a displacement of 1 km [backward].

Think about it

Can displacement be equal to distance?

Can displacement be greater than distance?


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10 2 3 4 5 6 7 8 9 1012345678910

Vectors in 1 – Plane

• 1 – plane means the vectors are in a line, without any bends

• Left – Right is 1‐ plane, as is North – South

Ex) 5 m [left], 2 m [right], 4 m [right] (note: right is considered positive, left negative)

distance :

displacement:

• vectors can also be sketched on a number line

• vectors are always drawn from the previous tip


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Vectors in 2‐ Planes

• Warning: will require the use of Pythagorean theorem and right angle trigonometry

• We will leave the trig out in the introductory lesson

• 2‐ planes means that we will be turning (ex. North then East)

Ex) 4 m [east] then 3 m [north]

Remember that we start at the tip of the previous vector

Using northeast (or southwest, or up‐right) as a direction is a big no‐no, but we will allow it for today.

Think about it

What might be the problem with simply giving a direction as northeast?

Practice Questions:

Find the magnitude and direction of each of the following:

1) 4 m [S], 2 m [E]

2) 5 km [N], 12 km [W]

3) 7 km [W], 2 km [S]

These can also be drawn to scale and measured. Try it yourself using 1 cm to represent 1 m. It will give the same answers.


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Trigonometric Ratios SohCahToaAngles and Direction

• At the moment, we are only concerned with finding angles (not side lengths) and so we will only use inverse trig functions

• On your calculator you will most likely has a second function or shift key that will need to be used

• For now, we will be using tangent (tan) as the sides we will be drawing will always be the opposite and the adjacent sides of the triangle

• When working with trig functions, keep your working to 4 decimal places until the end.

Ex) Find the measure of Ө (theta) in each.

4

2Ө

1) 7

9

Ө2)

http://www.youtube.com/watch?v=VRz2d5yedsg&safety_mode=true&persist_safety_mode=1&safe=active


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Displacement in 2 – Planes

• When reporting the angle, there are two methods used.

• The simplest (but my least favourite) is to write the first direction travelled, followed by the angle, then finishing with the second direction.

• The second method involves stating the angle, then the direction the angle turned to and form what direction it turned from (sounds worse than it is)

25º

• This angle could be reported as [W 25º N] or [25º N of W]

• Note that in each the position of the directions is simply switched.

Practice Questions

State the direction in each case.

1) 2)

3) 4)

15º

35º

3 m

5 m

Ө 2 m

1 m

Ө

• For extra practice, go back to the questions from yesterday and give the proper direction.

Complete Worksheet 1 (Displacement Vectors) and insert it into your portfolio!


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Distance / Displacement & Speed / VelocityFrom 1206:

• distance has the symbol “d”• displacement has the symbol “ ”• note the arrow over the d in displacement to indicate it is a vector• similarly, speed and velocity are v and and have the following

definitions

• since we are dividing a value in meters by a value in seconds the standard unit for speed or velocity is meters per second or m/s

• if the units are written in kilometers and hours, then the speed / velocity will be calculated in km / hr (this is fine for now, but will cause trouble later)

• note that speed is related to distance while velocity is related to displacement

Think about it

Which would be higher: an object’s speed or velocity?

”• displacement has the symbol “

Which would be higher: an object’s speed or velocity?

Think about it

displacement• note that speed is related to distance while velocity is related to

cause trouble later)velocity will be calculated in km / hr (this is fine for now, but will

• if the units are written in kilometers and hours, then the speed /

standard unit for speed or velocity is meters per second or m/s• since we are dividing a value in meters by a value in seconds the

definitions and have the following • similarly, speed and velocity are v and

• note the arrow over the d in displacement to indicate it is a vector

• distance has the symbol “d”

From 1206:Distance / Displacement & Speed / Velocity

Ex) Jeff walks 3 m [E] then 5 m [W] in 10 s.

a) What distance did he travel?

b) What was his displacement?

c) What was his speed?

d) What was his velocity?

• as in the above example, displacement and velocity always have the same direction

• in formal settings displacement and velocity need to have a stated direction (unless you are asked for magnitude only)


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Practice Questions

For each question, find the

a) distance

b) displacement

c) speed

d) velocity

1) Arnold travels 18 km [W] and then 8 km [E] in a time of 2.0 hours.

2) Henry travels 50 m [N] and then 25 m [E] in a time of 25s.

Think about it

How can you have an average velocity of zero?


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Graphical Analysis

Go to http://phet.colorado.edu/en/simulation/moving‐man and complete Worksheet 2: Sketching Graphs.

Be sure to put the worksheet in your portfolio when completed.

http://www.youtube.com/watch?v=Rb-hxkCwdcU&safety_mode=true&persist_safety_mode=1&safe=activehttp://phet.colorado.edu/en/simulation/moving-man


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Speed

Position – Time Graphs (Uniform Motion)

• it is typical to graph displacement (or position) over a period of time, however we “could” also graph distance (watch for the arrow)

• slope, or steepness, of any line represents the rate of change

• for a displacement (position) – time graph, the rate of change is velocity

• the steeper the line, or greater the slope, the faster the object is travelling

Think About It

What would the slope of a distance – time graph be?

• Describe the following graphs

d

t

d

t

d

t

• All of these graphs, with the exception of the first, show uniform motion / uniform velocity

• This means that there are discrete sections with no acceleration, or in other words that the motion occurs at a steady rate

• Any changes are indicated by sharp corners, not gradual bends


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Position – Time Graphs (Uniform Acceleration)

• Involve a steady change in velocity.

• As a result, these position – time graphs has discrete curved sections

• Tangents drawn to the curves can give the slope, and therefore velocity, at any given point so that we can see how the velocity changes over time.

• Describe the motion in the following graphs.

d

t

d

t

d

t

d

t

• As a reminder, positive acceleration will generate a “smile” while negative acceleration gives a “frown”

http://www.youtube.com/watch?v=WShxojeoor8&safety_mode=true&persist_safety_mode=1&safe=active


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Instantaneous

Values from Position Time Graphs

• For those unfamiliar with slope, it is calculated by the following equation

• On a position time graph, the slope between any two points is the average velocity over that time frame

• The slope of any continuous, straight section is the instantaneous velocity of any point on that section

• Average velocity is the total displacement over the total time

• Instantaneous velocity is the velocity at a particular point

Think About It

Does a car’s speedometer show average velocity or instantaneous velocity?


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What is the average velocity from 2 – 4 seconds?What is the average velocity from 0 – 3 seconds?

Complete Worksheet 3 – Displacement Time Graphs and place it in your portfolio.


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Acceleration is zero

Constant velocity

Travels in positive direction

Acceleration is negative

Velocity starts positive, hits zero, then goes negative

Travels forward, then backward

Acceleration is positive

Starts from rest, speeds up

Travels forward

Acceleration

v

tt

v v

t

Velocity – Time Graphs

Think about it

What is the rate of change of velocity over time?

• For uniform motion / velocity or uniform acceleration, the equation for acceleration is

• Since acceleration is find by dividing a quantity measured in m/s by one measured in s, the unit is m/s/s or m/s2

• The slope of a velocity – time graph will also give acceleration

Describe the motion in each graph.


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Calculating Acceleration (from Velocity Time Graph)

• Same as velocity from displacement – time graph

1)

2)


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Displacement from Velocity Time Graph

Think About It

During which graph would there be more displacement?

• The actual displacement can be calculated rearranging the normal, uniform motion equation


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Think About It (again)

During which graph would there be more displacement?

• In this case there is acceleration, and so we cannot simply use the normal equation (at least not directly)

• Since the line represents a continuous motion, the average velocity can be found by getting the average of the initial (first) and final (second) velocities

• This ONLY works with uniform acceleration

• The actual displacements for each graph is as follows:


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Area

• While using area may not be necessary for the previous graphs, it will be very useful for more complex arrangements.

• Simply cut the given section into a series of rectangles and triangles. The area is always measured back to the x‐axis

What is the total displacement of each graph?

1)

2)

3)

Complete Worksheet 4 – Velocity Time Graphs and place it in your portfolio

http://www.youtube.com/watch?v=d-_eqgj5-K8&safety_mode=true&persist_safety_mode=1&safe=active


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Core Lab 1: Acceleration due to Gravity

• If you miss a lab, you must complete an alternative assessment (as with any other assessment)

• Most labs will be completed in groups (alternative assessments will be individual)

• Core labs will require a lab report (one per group) that will either be used for evaluation or will be placed in your portfolio

Sample Lab Report (does not include everything, but gives general idea)

• Lab reports must include:

o Introduction (includes materials and basic idea of lab)

o Procedure (includes your steps and sketches of setup)

o Data / Observations (includes raw data)

o Analysis (includes calculations, graphs and questions)

o Conclusion(includes closing statement, sources of error, improvements, etc)

Web Alternative

• This lab will use Tracker, a freeware video analysis tool available at http://www.cabrillo.edu/~dbrown/tracker/

http://lectureonline.cl.msu.edu/~mmp/labs/samplelab/sample.htmhttp://lectureonline.cl.msu.edu/~mmp/labs/labdrop/lab.htm


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Standard Units

• when using equations, it is important that all values are in standard units

distance (m)

time (s)

speed (m/s)

Ex) A skydiver hits a maximum speed of 864 km/hr. What is his max speed in m/s?

Ex 2) The speed of sound is 340 m/s. What is this in km/hr?

acceleration (m/s2)

• in situations involving no acceleration, units may be left in kilometers, hours and km/hr if desired

Ex 3) A car travels 180 km in 90 minutes. What is its average speed?

Complete in m/s Complete in km/hr


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Scientific Notation

• a short way of recording values using a base ten exponent

• most calculators can handle this for you if you locate the proper button

• try to locate an “EE”,”Exp”, or “10x” button

• do not get in the habit of typing in the full value as it will cause trouble later

Converting from Scientific Notation

• positive exponent, move that number of places right

• negative exponent, move that number of places left

Converting to Scientific Notation

• move decimal to left, positive exponent (big number)

• move decimal to right, negative exponent (small number)

http://www.youtube.com/watch?v=AWof6knvQwE&safety_mode=true&persist_safety_mode=1&safe=active


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I'll be 19.5 minutes It's 109 km away I lost 27.8 lbs I lost 30.0 lbs

Significant Digits

Think About It

Do you ever use numbers in a way that they are not meant to be precise?

• Significant digits allows values to be calculated in such a way that they are accurate and precise

• this is mainly a lab based skill and often does not make sense in terms of answering random questions

• in general, when measuring values we should measure one more place than we can accurately see

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0 1 2 3 4 5 6 7 80°

• changing units can also complicate the process ( 1 m should be as precise as 100 cm)

Three Basic Rules

• all non‐zeros are significant

• trailing zeros without a decimal are not significant

• leading zeros are not significant

Ex)

1. 123

2. 1.05

3. 0.008

4. 0.0080

5. 20.000

6. 20 000

Think about it

If we say “It takes about 1 hour” what times could we be referring to?


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Where The Heck To Round?

Addition / Subtraction

• Go with the lowest number of places after the decimal

• Technically based on place value

Ex) 1.5 + 1.25

Ex 2) 141 – 0.75 + 1.8

Multiplication / Division (and exponents and roots for that matter)

• Round final answer to the least amount of SD

• The lazy method does this for all calculations

Ex) 2.5 x 1.85

Ex2) 2 x 0.0057 / 1.28

http://www.youtube.com/watch?v=kB2szfcwu1A&safety_mode=true&persist_safety_mode=1&safe=active


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Mixed Operations (non – lazy)

• Only use if specifically asked a question about significant digits

• A little tricky, but not too bad if you are well organized

o Complete question without rounding (at all!)

o Write down all steps

o Follow individual rules through steps

Ex) 7.58 + 1.8 x 10.5

Ex 2) 12.5 x 5.70 – 6.8

Complete Worksheet 5 – Kinematics Pre‐Skills and put it in your portfolio.

Attachments

Physics 2204 Worksheet 1 Displacement Vectors.doc

Physics 2204 Worksheet 2 Sketching Graphs.doc

Physics 2204 Worksheet 3 Displacement Time Graphs.doc

Physics 2204 Worksheet 4 Velocity Time Graphs.doc

Physics 2204 Worksheet 5 Kinematics PreSkills.doc

Physics 2204: Worksheet 1 – Displacement Vectors

1. Sketch the following vectors.

a. 24º E of W

b. N 65º E

c. 15º W of S

2. Sketch the vectors and calculate the final displacement. Remember to include both the magnitude and direction.

a. 3 km [N] + 2 km [S]

b. 6 m [E] + 6 m [N]

c. 2.7 km [S] + 1.5 km [E] + 2.4 km [W]

SMART Notebook

Physics 2204: Worksheet 2 – Sketching Graphs

Name: ____________________

Go to http://phet.colorado.edu/en/simulation/moving-man

Once loaded, click charts and complete the following.

Part A: Uniform Motion / Uniform Velocity (no acceleration)

For this section, be sure to keep the acceleration set at 0 m/s2

1. Run a few trials with positive velocity. Draw sketches of the graphs below.

d =

v =

a = 0

displacement – time graph

velocity – time graph

acceleration – time graph

d =

v =

a = 0




d =

v =

a = 0




2. Do the same with negative velocity. Draw sketches of the graphs below.

d =

v =

a = 0




d =

v =

a = 0




d =

v =

a = 0




3. What do you expect a graph with a velocity of zero to look like? Run a simulation to verify.

Part B: Uniform Acceleration

4. Run a few trials with positive acceleration. Use positive and negative velocity and try varying the starting position. Draw sketches of the graphs below.

d =

v =

a =




d =

v =

a =




d =

v =

a =




5. Do the same with negative acceleration. Draw sketches of the graphs below.

d =

v =

a =




d =

v =

a =




d =

v =

a =




6. What would be your definition of acceleration?

SMART Notebook

Physics 2204: Worksheet 3 - Position – Time Graphs

Name: ________________

1) Find the average velocity from:

Series 1

-224681012

2

4

6

8

10

12

14

16

18

20

22

24

Time (s)

Distance (m)

a) 0-2 seconds

b) 7 – 10 secondsc) 2 – 8 seconds

2) Find the average velocity from:

Series 1

-224681012

-8

-6

-4

-2

2

4

6

8

Time (s)

Distance (m)

a) 0-2 seconds

b)4- 9 seconds

c) 0 –12 seconds

3) When is the object stopped in:

a) Graph 1

b) Graph 2

_1377603612.unknown

_1377603611.unknown

SMART Notebook

Physics 2204: Worksheet 4 – Velocity Time Graphs

Name: ___________________

123456789101112

-4

-3

-2

-1

1

2

3

4

5

6

time (s)

velocity (m/s)

1) What is the average velocity between 0 – 3 seconds?

2) What is the acceleration between 7 – 12 seconds?

3) What is the total displacement between 0- 7 seconds?

4) What is total distance travelled between 0 – 10 seconds?

5) When is the object stopped?

_1433156647.unknown

SMART Notebook

Physics 2204: Worksheet 5 – Kinematics Pre-Skills

Name: _______________________

1. Convert to standard units. Keep the same number of significant digits.

a. 1.50 km

b. 2.8 hours

c. 58 cm

d. 120 km/hr

2. Convert to scientific notation with 2 significant digits.

a. 278 000

b. 35 000

c. 0.0006

d. 0.00309

3. Complete the following with proper rounding / significant digits.

a. 2.6 x 8.56

b. 0.96 + 0.356

c. 4.79 + 2.6 x 18

d. 7.9 / 2.8 + 1.75

SMART Notebook

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Documents

Unit 1 : Kinematics 2204 unit 1...Distance VS Displacement Distance : total ground covered travelling from A to B For example: Walking forward 3 km, then back 4 km gives a distance