Unit 1

Chapter 1

Measurements

Units of Measurement

Measurement

You are making a measurement when you

Check you weight

Read your watch

Take your temperature

Weigh a cantaloupe

What kinds of measurements did you make today?

Standards of Measurement

When we measure, we use a measuring tool to compare some dimension of an object to a standard.

Some Tools for Measurement

Units of MeasurementsMKS: meters (m), Kilogram (kg), second (s) kilometer (km), hour (h)

CGS: centimeter (cm), gram (g), second (s)

FPS: foot (ft.), pound (lb.), second (s) miles (mi.), hour (h)

Learning Check

From the previous slide, state the tool (s) you would use to measureA. temperature ____________________B. volume ____________________

____________________C. time ____________________D. weight ____________________

Solution From the previous slide, state the tool (s) you would use to measureA. temperature thermometerB. volume measuring cup,

graduated cylinderC. time watchD. weight scale

Learning Check

What are some U.S. units that are used to measure each of the following?

A. length

B. volume

C. weight

D. temperature

Solution Some possible answers are

A. length inch, foot, yard, mile

B. volume cup, teaspoon, gallon, pint,

quart

C. weight ounce, pound (lb), ton

D. temperature F

Metric System (SI)

Is a decimal system based on 10

Used in most of the world Used by scientists and

hospitals

Units in the Metric System

length meter m

volume liter L

mass gram g

temperature Celsius °C

Stating a Measurement

In every measurement there is a

Number

followed by a

Unit from measuring device

Learning Check

What is the unit of measurement in each of the following examples?

A. The patient’s temperature is 102°F.

B. The sack holds 5 lbs of potatoes.

C. It is 8 miles from your house to school.

D. The bottle holds 2 L of orange soda.

Solution

A. °F (degrees Fahrenheit)

B. lbs (pounds)

C. miles

D. L (liters)

Learning Check Identify the measurement in metric units. A. John’s height is1) 1.5 yards 2) 6 feet 3) 2

meters

B. The volume of saline in the IV bottle is1) 1 liters 2) 1 quart 3) 2 pints

C. The mass of a lemon is1) 12 ounces 2) 145 grams3) 0.6 pounds

The Seven Base SI Units

Quantity Unit Symbol

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of Substance

mole mol

Luminous Intensity candela cd

Electric Current ampere a

SI Unit Prefixes - Part I

Name Symbol Factor

tera- T 1012

giga- G 109

mega- M 106

kilo- k 103

hecto- h 102

deka- da 101

SI Unit Prefixes- Part II

Name Symbol Factor

deci- d 10-1

centi- c 10-2

milli- m 10-3

micro- μ 10-6

nano- n 10-9

pico- p 10-12

femto- f 10-15

Derived SI Units (examples)Quantity unit Symbol

Volume cubic meter m3

Density kilograms per cubic meter

kg/m3

Speed meter per second m/s

Newton kg m/ s2 N

Energy Joule (kg m2/s2) J

Pressure Pascal (kg/(ms2) Pa

SI Unit Prefixes for LengthName Symbol Analogy

gigameter Gm 109

megameter Mm 106

kilometer km 103

decimeter dm 10-1

centimeter cm 10-2

millimeter mm 10-3

micrometer μm 10-6

nanometer nm 10-9

picometer pm 10-12

Scientific Notation

M x 10n

M is the coefficient 1<M<1010 is the basen is the exponent or power

of 10

Factor-Label Method of Unit Conversion: Example

Example: Convert 789m to km:

789m x 1km =0.789km= 7.89x10-1km

1000m

Limits of Measurement

Accuracy and Precision

Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: AccuracyWho is more accurate when measuring a book that has a true length of 17.0cm?

Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision

Who is more precise when measuring the same 17.0cm book?

Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Significant FiguresThe significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

Finding the Number of Sig Figs:

When the decimal is present, start counting from the left.

When the decimal is absent, start counting from the right.

Zeroes encountered before a non zero digit do not

count.

Measuring Tools

Vernier caliper Vernier caliper is a measuring device used to

measure precise increments between two points.

Micrometer Micrometer is a measuring device used for

precisely measuring thickness, inner and outer diameter, depth of slots.

SWG A gauge for measuring the diameter of wire,

usually consisting of a long graduated plate with similar slots along its edge.

Vernier caliper

Function To measure smaller distances Can measure up to .001 inch or .01mm.

Features Larger, lower jaws are designed to measure

outer points e.g. diameter of a rod. Top jaws are designed to measure inside points

e.g. size of a hole. A rod extends from the rear of the caliper and

can be used to measure the depth.

Structure of Vernier caliper

Structure of the Vernier caliper Main Scale

Main scale is graduated in cm and mm.

Vernier Scale It slides on the main scale. On Vernier scale 0.9cm is divided into 10 equal

parts.

Jaws Two inside jaws (Upper) Two outside jaws (Lower)

Least Count

Least count (L.C) is the smallest reading we can measure with the instrument.

L.C = one main scale division – one vernier scale division

L.C = 1mm – 0.09mmL.C = 0.1mm = 0.01cm

Least Count = Value of the smallest division on MS/ Total number of division on VSL.C = 1mm / 10 = 0.1 cm / 10 = 0.01cm

Reading of the Instrument

Reading of the instrument = MS div + (coinciding VS div x L.C)

= 3.2 + (3 x 0.01) = 3.2 + 0.03 = 3.23 cm

Micrometer

Function Micrometer allows the measurement of the size

of the body i.e. thickness, depth, inner/outer diameter.

Features Two jaws (one fixed, one movable) Spring loaded twisting handle Easy to use and more précised Can measure up to .001cm

Structure of the Micrometer

Structure of Micrometer

Jaws 2 jaws (one fixed, one movable)

Circular Scale Movable jaw is attached to a screw, scale on this

screw is called Circular scale. Either 50 or 100 divisions

Linear Scale Horizontal Scale

Structure of Micrometer

Frame The C-shaped body that holds the anvil and sleeve in constant

relation to each other. Anvil

The jaw which remains stationary. Spindle

The jaw which moves towards the anvil. Lock Nut

A lever, one can tighten to hold the spindle stationary. Sleeve

The stationary round part with the linear scale on it. (Main Scale)

Thimble Thimble rotates around the sleeve.

Ratchet Stop Device on end of handle that limits applied pressure by slipping

at a calibrated torque.

Pitch of Micrometer

When the head of the micrometer rotate through one rotation, called pitch of the micrometer.

The screw moves forward or backward 1mm on the linear scale.

Pitch of Micrometer = distance on linear scale / one rotation

Pitch of Micrometer = 1/1 = 1mm

Reading of the Instrument

Reading of the instrument = MS div + (coinciding CS div x L.C)

= 8+ (12 x 0.01) = 8 + 0.120mm = 8.120 mm = 8120 µm

Scalars A scalar quantity is a quantity that has magnitude only and has no direction in space

Examples of Scalar Quantities:

Length Area Volume Time Mass

Vectors A vector quantity is a quantity that has both magnitude and a direction in space

Examples of Vector Quantities:

Displacement Velocity Acceleration Force

Vector Diagrams Vector diagrams are shown using an arrow

The length of the arrow represents its magnitude

The direction of the arrow shows its direction

April 11, 2023

Speed is defined as the distance travelled per unit time and has the units of m/s or ms-1.

Distance, Speed and Time

April 11, 2023

Speed = distance (in metres)

time (in seconds)

D

TS

1) Dave walks 200 metres in 40 seconds. What is his speed?

2) Laura covers 2km in 1,000 seconds. What is her speed?

3) How long would it take to run 100 metres if you run at 10m/s?

4) Steve travels at 50m/s for 20s. How far does he go?

5) Susan drives her car at 85mph (about 40m/s). How long does it take her to drive 20km?

April 11, 2023

Speed is defined as the distance travelled per unit time and has the units of m/s or ms-1.

Velocity is speed in a given direction and has the same units as speed.

Speed vs. VelocityApril 11, 2023

Speed is simply how fast you are travelling…

Velocity is “speed in a given direction”…

This car is travelling at a speed of 20m/s

This car is travelling at a velocity of 20m/s east

April 11, 2023

Speed is defined as the distance travelled per unit time and has the units of m/s or ms-1.

Velocity is speed in a given direction and has the same units as speed.

To calculate speed we use the equation:

Average speed = distance travelled/time taken = d/t

Distance is measured in metres (m) and time is measured inseconds (s).

The greater the distance travelled in a given time then the greater is the speed.

April 11, 2023

A useful way to illustrate how the distance throughout a journey varies with time is to plot a DISTANCE AGAINST TIME graph.

This gives us a visual representation of how the journey progressedand allows us to see quickly how long each stage of the journey tookcompared with the other stages.

The steepness (gradient) will also give us the speed.

The following graphs show how the shape of distance-time graphsmay vary and how to interpret them

April 11, 2023

Distance

Time00

A

B C

AB- constant speed

BC - stationary

Gradient = rise/run = speed

Rise

Run

Distance - Time GraphsDistance - Time Graphs

April 11, 2023

DISTANCE is a SCALAR quantity and has size only but DISPLACEMENT is a VECTOR quantity and has size (or magnitude) and DIRECTION.

10 metres is a distance (size only) but 10 metres due south (size and direction) is a vector quantity.

If we use DISPLACEMENT instead of distance then the graph will also give an indication of the direction taken with respect to its starting point.

April 11, 2023

Displacement

Time00

AB - constant velocity(speed & direction)

BC - stopped

CD - Returningto its starting positionat a constantvelocity

A

B C

D

Distance - Time GraphsDistance - Time Graphs

Distance-time graphsApril 11, 2023

40

30

20

10

0 20 40 60 80 100

4) Diagonal line

downwards =

3) Steeper diagonal line =1) Diagonal line =

2) Horizontal line =

Distance

(metres)

Time/s

April 11, 2023

40

30

20

10

020 40 60 80 100

1) What is the speed during the first 20 seconds?

2) How far is the object from the start after 60 seconds?

3) What is the speed during the last 40 seconds?

4) When was the object travelling the fastest?

Distance

(metres)

Time/s

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

(a) Plot a distance-time graph.(b) What was the snail’s speed before lunch?(c) What was the snail’s speed after lunch?

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

4

8

12

16

800 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

4

8

12

16

0 80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

(a) See graph(b) Speed before lunch = initial gradient

= rise/run= 8/80= 0.1m/s

4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

4

8

12

16

0 80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

(a) See graph(b) Speed before lunch = initial gradient

= rise/run= 8/80= 0.1m/s

4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away.

Plot a distance-time graph.What was the snail’s speed before lunch?What was the snail’s speed after lunch?Distance (m)

Time (s)0

0

(a) See graph(b) Speed before lunch = initial gradient

= rise/run= 8/80= 0.1m/s

(c) Speed after lunch = final gradient= rise/run = 8/120= 0.067 m/s4

8

12

16

80 160 240

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

Consider a car starting from rest and its speed is increasing continuously.

Distance (m)

Time (s)0

200

400

600

800

200 40 60

April 11, 2023

Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples

Consider a car starting from rest and its speed is increasing continuously.Find the speed of the car at 40 seconds after the start of the journey.

Distance (m)

Time (s)0

200

400

600

800

200 40 60

April 11, 2023

Acceleration is defined as the change in velocity in unit time and has the units m/s/s or m/s2 or ms-2

Acceleration is a vector quantity and so has size and direction.

Velocity - Time GraphsVelocity - Time Graphs

To calculate acceleration we use the equation:Average acceleration = change in velocity/time taken

= (final velocity – initial velocity)/time taken

= (v – u)/t

Velocity is measured in metres per second (m/s) and time is measured in seconds (s).

The greater the change in velocity in a given time then the greater is the acceleration.

Acceleration

April 11, 2023

V-U

TA

Acceleration = change in velocity (in m/s)

(in m/s2) time taken (in s)

1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration?

2) A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by?

3) A car accelerates from 10 to 20m/s with an acceleration of 2m/s2. How long did this take?

4) A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?

April 11, 2023

A useful way to illustrate how the velocity throughout a journey varies with time is to plot a VELOCITY AGAINST TIME graph.

This gives us a visual representation of how the journey progressedand allows us to see quickly how long each stage of the journey tookcompared with the other stages.

.

Velocity - Time GraphsVelocity - Time Graphs

The steepness (gradient) will also give us the ACCELERATION.

The area under a velocity-time graph gives us the distance travelled.

The following graphs show how the shape of velocity-time graphsmay vary and how to interpret them

April 11, 2023

Velocity

Time00

A

B C

AB- constant acceleration

BC - constant velocity

Gradient = rise/run = acceleration (m/s2)

Rise

Run

Velocity - Time GraphsVelocity - Time Graphs

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Velocity

Time00

A

B

C

D E

Constant Acceleration

Constant Velocity

At B,C & D there isinstantaneous change in acceleration

Area Under Graph = Total Distance Travelled

Velocity - Time GraphsVelocity - Time Graphs

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(a) Constant Velocity

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(a) Constant Velocity

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

Distance travelled= area under graph= area of rectangle= length x breadth= 8 x 8= 64m

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(b) Uniform Acceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(b) Uniform Acceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(b) Uniform Acceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

Distance travelled= area under graph= area of triangle= ½ base x height= ½ 8 x 8= 32 m

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(b) Uniform Acceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

Distance travelled= area under graph= area of triangle= ½ base x height= ½ 8 x 8= 32 m

Acceleration = gradient= rise/run= 8/8= 1 ms-2

April 11, 2023

Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(c) Uniform Deceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(c) Uniform Deceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

Distance travelled= area under graph= ½ base x height= ½ 10 x 10= 50m

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(c) Uniform Deceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

Distance travelled= area under graph= ½ base x height= ½ 10 x 10= 50m

Acceleration = gradient= rise/run= -10/10= -1 ms-2

(Deceleration = +1 ms-2

April 11, 2023

A car starts from rest and accelerates uniformly to 20m/s in 10 seconds.It travels at this velocity for a further 30 seconds before decelerating uniformly to rest in 5 seconds.(a) draw a velocity - time graph of the car’s journey(b) calculate the car’s initial acceleration(c) calculate the car’s final deceleration(d) calculate the total distance travelled by the car(e) calculate the distance travelled by the car in the final 25 seconds

Velocity - Time Graphs: ExampleVelocity - Time Graphs: Example

April 11, 2023

Velocity

Time00

20

(m/s)

(s)10 40 45

Initial acceleration= initial gradient= rise/run= 20/10= 2m/s2

Velocity - Time GraphsVelocity - Time Graphs

April 11, 2023

Velocity

Time00

20

(m/s)

(s)10 40 45

final acceleration= final gradient= rise/run= -20/5= -4m/s2

Velocity - Time GraphsVelocity - Time Graphs

April 11, 2023

Velocity

Time00

20

(m/s)

(s)10 40 45

A B C

Total distance travelled = total area under graph= area A + B + C = ½ x 10 x 20 + 30 x 20 + ½ x 5 x 20= 100 + 600 + 50 = 750m

Velocity - Time GraphsVelocity - Time Graphs

April 11, 2023

Velocity

Time00

20

(m/s)

(s)10 40 45

C

Distance travelled in final 25s = part area under graph= area D + C = 20 x 20 + ½ x 5 x 20= 400 + 50 = 450m

D

20

Velocity - Time GraphsVelocity - Time Graphs

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Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples

(b) Uniform Acceleration

Velocity (ms-1)

Time (s)

10

8

6

4

2

00 2 4 6 8 10

Distance travelled= area under graph= area of triangle= ½ base x height= ½ 8 x 8= 32 m

Acceleration = gradient= rise/run= 8/8= 1 ms-2

Velocity-time graphs

April 11, 2023

80

60

40

20

0 10 20 30 40 50

Velocity

m/s

T/s

1) Upwards line =

2) Horizontal line =

3) Steeper line =

4) Downward line =

April 11, 2023

80

60

40

20

01) How fast was the object going after 10 seconds?

2) What is the acceleration from 20 to 30 seconds?

3) What was the deceleration from 30 to 50s?

4) How far did the object travel altogether?

10 20 30 40 50

Velocity

m/s

T/s

THE ACCELERATION OF FREE FALL

Questions: Do heavier objects fall faster than lighter ones

when starting from the same position? Does air resistance matter? If the free fall motion has a constant acceleration,

what is this acceleration and how was it found? How do we solve problems involving free fall?

Galileo (1564 – 1642) and the leaning tower of Pisa.

Air Resistance The force of friction or drag acting on an

object in a direction opposing its motion as it moves through air.

Hammer & Feather in the presence of air

Hammer & Feather in the absence of air

If the free fall motion has a constant acceleration, what is this acceleration and how was it found?

If there were no air resistance both objects would fall with the same downward acceleration ;9.8 m/s2.this is called the acceleration of free fall

The acceleration of free fall if represented by the symbol ‘g’.

Its value varies from one place on earth to another

Moving away from the earth and out into space ,g decreases

The value of g near the earth surafce is close to 10 m/s

How Fast?