MotionPhysics 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

Accuracy and PrecisionMaking 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.

Example: Golfing4 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!!

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

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, 3.000 are of the same value, but 3.000 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.

Types of Numbers

• numbers obtained through counting.

• These stand as is.

• numbers obtained through measurement.

• With these numbers we must determine how precise they are when we use them in calculations.

Exact Numbers Approximate Numbers

Determining Sig. Figs

• All non-zero integers are significant.

• Captive zeros are always significant.

• Leading zeros are NEVER significant.

• Trailing zeros in a decimal are significant.

• Assumed decimals are not significant.

Ex. 500

4 sig. figs

3 sig. figs

2 sig. figs

4 sig. figs

1 sig. figs

Ex. 256.5

Ex. 206

Ex. 0.0056

Ex. 25.00

RoundingWhen you are rounding numbers:

1. Consider how many sig fig.s you want to keep.2. Underline that number.3. Look to the number to the right of that number.4. If the number after the line is 5 or more, round

up.Ex. Round to 2 sig. fig.s

3.45 10.99= 3.5

5. If the number after the line is 4 or less, leave it alone.

Ex. Round to two sig. fig.s0.00423 6.8219

= 0.0042

= 11

= 6.8

Rules For Calculations:

• Do the math.

• The answer should contain the same number of decimal places as the number with the least decimal places.

Ex. 25.46 + 12.5 + 82.91 =

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. 0.14 x 98.54 x 12.5 =

only 2 sig. fig

170

Addition and Subtraction Multiplication and Division

120.87 172.445

Examples:

1. 12.58 cm + 0.125 cm + 10.47 cm =

= 23.18 cm

2. 25.78 m x 12.85 m =

5.8 m

= 57 m

23.175

57.11603448

Try These:

1. 2.365 + 5.8

2. 6.98 – 5.7124

3. 1.3333 + 5.4215

4. 5 – 2.6123

5. 8.23 + 0.65

1. 8.165 = 8.2

2. 1.2676 = 1.27

3. 6.7548

4. 2.3877 = 2

5. 8.88

Try These:

1. 2.365 x 5.8

2. 6.18 x 2.714

3. 1.3433 x 5.421

4. 5 ÷ 2.6123

5. 8.23 ÷ 0.65

13.717 = 14

16.77252 = 16.8

7.2820293 = 7.282

1.914022126 = 2

12.66153846 = 13

Metric System Review• 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

Prefixes

Ketchup has destroyed my

delicious chocolate milk

Examples

1. 12 cm = mm

120

2. 250 hg = kg

25

3. 54 L = mL

54 000

4. 3456 hm = km

345.6

5. 109 kg = dag

10 900

6. 0.678 g = cg

67.8

G . . M . . K h da m d c m . . µ . . n

Metric Mania Worksheet

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 4

1

quarters

dollar

1

4

dollar

quarters

Conversion Rules1. Write the number given (with units) and a multiplication sign

2. Write your conversion factor

- put the unit given on the bottom

- put the unit you want to get on the top

3. Work out the problem.

Convert 51.5 km into miles (1.6 km = 1mile)

= 32.187551.5km x

1.6

1

km

mile

1

1.6

mile

km

or

1

1.6

mile

km

= 32.2 miles

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 hoursWorksheet #1

= 500 hours

= 4.0 days

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

0.0000458

2.305 x 103

4.58 x 10-5

Scientific Notation• Rules:

1. First number (coefficient) is a number from 1-9

2. The first figure is always followed by a decimal point and then the rest of the digits.

3. 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.

Standard Notation Scientific Notation

1648

150000

0.000648

7840

0.00048

385000

557

0.00042

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

Expanded Notation

1. If you have a positive exponent, then move the decimal to the right.

Ex. 23.546 x 102 = 2354.6

2. If you have a negative exponent, then move the decimal to the left.

Ex. 23.546 x 10 -2 = 0.23546

Try the following:

Expanded Notation Scientific Notation

12 000 000

85 130

0.018

2000

0.0000345

876.5

1.2 x 107

8.513 x 104

1.8 x 10-2

2.0 x 103

3.45 x 10-5

8.765 x 102

Worksheet #3

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.

• Example 1: D = m Solve for m

V

Rearrange the formula so that the m is by itself on the left hand side:

m = D

V

• Example 2: D = m Solve for VV

To move V: - multiply by V on both sides

D = mV

To move D: - divide by D on both sides

V = Dm

Try the following:

1. y = mx + b Solve for xx = y-b

m

2. v = d Solve for dt

d = vt

3. s = r + dg Solve for rr = s – dg

4. C = Rf – s Solve for ff = C + s

RWorksheet #4

Section 9.5

Relating Speed to

Distance and Time

• 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 =

Average Speed

• 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, andthey had to stop at signs and lights during thetrip.

=

= 42.0 km/hr

= 42

• 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

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).

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

Examples

• Sally roller blades to school. It takes her 0.62 hours to travel 4.5 km. What is her average speed?

• d= 4.5 km

• t = 0.62 hrs

• v = ?

Vav = =

= 7.258064516

= 7.3 km/hr

• 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 = ?

∆t = = 2.25

= 2.3 hr

• Bison graze at an average speed of 110.0 m/h. If these bison graze for 7 hours/day then how far will the herd travel in 14 days?

• v = 110.0 km/hr

• t = 7 hrs a day for 14 days

• d = ?

14 days x = 98 hrs

∆d = x 98hrs

= 11 000 km

= 10 780

• You are travelling on a train a distance of 10.0 km. It takes 390.6 seconds. Determine the speed in km/h.

▫ (Hint: change seconds into hours first).

• d = 10.0 km

• t = 390.6 sec

• v = ?

390.6 sec x x =

= 0.1085 hrs

= 92.1658986

= 92.2 km/hr

Section 9.7

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.

Linear Graphs• Represents a direct relationship between distance and

time.

Recall the equation for a straight line: y = mx + bwhere: y = dependent variable (y-axis)

x = independent variable (x-axis)m = slope of the lineb = y intercept of line

Following the Speed formula becomes: d = vt + 0d = vt

where: d = distance (y-axis)t = time (x-axis)v = speed (slope of the line)

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.

Moving quickly - Moving slowly - Not movingLarge distance Short distance No distance over short time. overlong time. overtime.

Try this activity:

• \\Rural_310_fs\data\RURAL310\USERADM\jcacorn\Science 421\Power Points\distance_time_graphs.ppt

Line Graph Rules

1. The bigger the better. Use most of the graph paper to draw the graph. Leave large enough margins for writing.

2. 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.

3. Choose a suitable scale for each axis. Space numbers evenly, count by 2's, 5's, 10's, etc.

4. 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.

5. Be neat and accurate. Plot the points carefully.

6. 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.

Time (s)0 2 4 6 8 10 12 14

0

510

15

20

25

30

35Distance vs Time of Mrs. Huggan

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) ∆drun (change in x values) ∆t

(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 = 10.0 m/s5.0 s

x1 = 0

y1 = 0

x2 = 5.0

y2

=50.0

Slope = rise (change in y values) = (300.0 km – 0.0 km) run (change in x values) (5.0 h – 0.0 h)

= 300.0 km = 60.05.0 h

= 6.0 x 101 km/h

x1 = 0

y1 = 0

x2 = 5.0

y2 = 300.0

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.

Time (h)0 1 2 3 4 5 6 7 8

0

2

4

6

8

10

12

Average Speed (km/h)

A

B

C

D

Assignment:

• Read pages 362-364 and do # 1, 2, 3, 5, 6 on page 365.

Section 10.3

• Acceleration

▫ the rate of change in speed of an object.

• Acceleration (a) = Δv = vf - vi

t t

vf is the final speedvi is the initial speeda = average accelerationt = timeΔv = 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

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

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

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?

2. A car may accelerate from 0.0 km/h to 100.0 km/h in 6.0 s. What is the average acceleration of this car?

3. Kerry is moving at 1.8 m/s near the top of a hill. 4.2 s later, she is traveling at 8.3 m/s. What is her average acceleration?

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

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?

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?

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?

Example 1

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

Example 2

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

Section 10.4

• 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)

• Decreasing Acceleration

▫ Negative speed

▫ Slowing down

• No Acceleration

▫ Zero value

• Increasing Acceleration

▫ Positive speed

▫ Speeding up

A - decreasing speed

B - increasing speed

C - constant speed

D - slowly increasing speed

E - rapidly increasing speed

E

Make a GraphTime (s) Speed (m/s)

0 0

10 2

20 4

30 6

40 8

50 10 Time (s)0 10 20 30 40 50 60

0

2

4

6

8

10

12

Acceleration on a Bicycle

• 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 = areab = baseh = height

• If the area under the line is a rectangle, then the formula for area is

A = lw where: a = areal = lengthw = width

A

B

C

http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/ConstantAccel/ConstantAccel.html