Chapter 2: Kinematics in one Dimension

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Chapter 2 Kinematics in one Dimension

• Displacement
• Velocity
• Acceleration

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Multiplying Significant Figures

• Distance velocity x time
• Velocity 65.4mph
• Time 4.2 hours

• Distance274.7 or 275 or 2.7x102 miles

• When you multiply (or divide) you keep the number
  of significant figures that are equal to the
  quantity with the smallest number of significant
  figures.

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Importance of Units

• The 165 million dollars Mars Polar Lander

• Units help you figure out equations
• Speed in mph
• Density in kg/m3

• Units help you determine the correct solution

www.nasa.gov
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Units, Standards, and the SI System
Quantity Unit Standard
Length Meter Length of the path traveled by light in 1/299,792,458 second
Time Second Time required for 9,192,631,770 periods of radiation emitted by cesium atoms
Mass Kilogram Old def (until Summer 2019) Platinum cylinder in International Bureau of Weights and Measures, in Paris. New def the international prototype of the kilogram (IPK). Alternatively, in the energy equivalence relations E hf mc2 eV kT the Planck constant h, the speed of light c, the elementary charge e, and the Boltzmann constant k can also be reference quantities since they are invariants with specific values.
https//www.nist.gov/si-redefinition/meet-constant
s
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Units, Standards, and the SI System
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Units, Standards, and the SI System
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Units, Standards, and the SI System
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Units, Standards, and the SI System
We will be working in the SI system, in which the
basic units are kilograms, meters, and seconds.
Quantities not in the table are derived
quantities, expressed in terms of the base units.
Other systems cgs units are centimeters, grams,
and seconds. British engineering system has force
instead of mass as one of its basic quantities,
which are feet, pounds, and seconds.
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Converting units

• Problem 11.
• (I) Write the following as full (decimal) numbers
  with standard units (a) 286.6 mm, (b) 35mV,
• (c) 760 mg, (d) 60.0 ps, (e) 22.5 fm, (f) 2.50
  gigavolts.

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Problem 11 Solutions
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Converting units

• Problem 15. (II) What is the conversion factor
  between
• (a) ft2 and yd2
• (b) m2 and ft2
• 1yd3ft and 1m3.28ft

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Problem 15 Solutions
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Converting units

• Write this in miles/s and miles/hour
• 30.0 km/h ?
• 1 km 0.6214 miles
• 1 mile1.6093km
• How many Us dollars is in 220 Canadian dollars?
• 220 Canadian Dollars ?
• 1 US dollar 1.31 Canadian dollar

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Converting units
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Problem 65 Solutions
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Question

• 1 atm 1.013 x105 Pa 14.70 lb/in2
• If you want to convert 0.46 atm to Pa you should
• Multiply 0.46 atm by 14.70 lb/in2
• Multiply 0.46 atm by 1.013 x105 Pa
• Divide 0.46 atm by 14.70 lb/in2
• Divide 0.46 atm by 1.013 x105 Pa

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Converting units

• Multiplying by 1 leaves a quantity unchanged.
• 1 can be represented as
• Choose form for 1 for which units match.

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Prefixes

• Prefixes correspond to powers of 10
• Each prefix has a specific name
• Each prefix has a specific abbreviation

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Prefixes

• The prefixes can be used with any base units
• They are multipliers of the base unit
• Examples
• 1 mm 10-3 m
• 1 mg 10-3 g

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Fundamental and Derived Quantities

• In mechanics, three fundamental or base
  quantities are used
• Length
• Mass
• Time
• Will also use derived quantities
• These are other quantities that can be expressed
  as a mathematical combination of fundamental
  quantities

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Density

• Density is an example of a derived quantity
• It is defined as mass per unit volume
• Units are kg/m3

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Order of Magnitude Rapid Estimating
A quick way to estimate a calculated quantity is
to round off all numbers to one significant
figure and then calculate. Your result should at
least be the right order of magnitude this can
be expressed by rounding it off to the nearest
power of 10.
Diagrams are also very useful in making
estimations.
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Order of Magnitude Rapid Estimating
Example 1-6 Thickness of a page.
Estimate the thickness of a page of your
textbook. (Hint you dont need one of these!)
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Chapter 2 Kinematics in one Dimension

• Displacement
• Velocity
• Acceleration

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Chapter 2 Kinematics in one Dimension
Coordinate Axis

• In Physics we draw a set of coordinate axis to
  represent a frame of reference.
• In one dimensional axis coordinate, the position
  of an object is given by its x or y.

y
x
-x
o
-y
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Position on a line

• Reference point (origin)
• position
• Distance
• Direction

• The position of Charlotte in reference to Fort
  Mill ( Fort Mill is the origin)
• Symbol for position x
• SI units meters, m

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Displacement on a line

• Change of position is called Displacement

xf
xi
Displacement is a vector quantity It has
magnitude and direction
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Displacement

• Defined as the change in position during some
  time interval
• Represented as ?x
• SI units are meters (m) ?x can be positive or
  negative
• Different than distance the length of a path
  followed by a particle.
• Displacement has both a magnitude and a direction
  so it is a vector.

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Example

• Mary walks 4 meters East, 2 meters South, 4
  meters West, and finally 2 meters North. The
  entire motion lasted for 24 seconds. Determine
  the displacement and distance Mary travelled.

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Vectors and Scalars

• Vector quantities need both a magnitude (size or
  numerical value) and direction to completely
  describe them
• Will use and - signs to indicate vector
  directions
• Scalars quantities are completely described by
  magnitude only

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Average Speed

• Average speed distance traveled/ time elapsed
• Example if a car travels 300 kilometer (km) in 2
  hours (h), its average speed is 150km/h.
• Not to confuse with average velocity.
• Average speed is a scalar

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Average Velocity

• The average velocity is rate at which the
  displacement occurs
• The SI units are m/s
• Is also the slope of the line in the position
  time graph

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Average Velocity, cont

• Gives no details about the motion
• Gives the result of the motion
• It can be positive or negative
• It depends on the sign of the displacement
• It can be interpreted graphically
• It will be the slope of the position-time graph

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Average Speed and Average Velocity
Speed is how far an object travels in a given
time interval
Velocity includes directional information
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Not to Confuse

• Speed is a number a scalar
• Velocity is a vector with a magnitude and a
  direction

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Average velocity from a graph of x(t)
v(t) slope of x(t)
Position (x)
Time (t)
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Average Speed
Example 2-2 Distance a cyclist travels. How far
can a cyclist travel in 2.5 h along a straight
road if her average speed is 18 km/h?
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Example 1

• While on Vacation Lisa traveled a total distance
  of 440 miles her trip took 8 h , what was her
  average speed?

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Example 1 solution

•  

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Example 2

• Mary walks 4 meters East, 2 meters South, 4
  meters West, and finally 2 meters North. The
  entire motion lasted for 24 seconds. Determine
  the average speed and the average velocity.

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• Mary walked a distance of 12 meters in 24
  seconds thus, her average speed was 0.50 m/s.
• However, since her displacement is 0 meters, her
  average velocity is 0 m/s.
• Remember that the displacement refers to the
  change in position and the velocity is based upon
  this position change. In this case of the Marys
  motion, there is a position change of 0 meters
  and thus an average velocity of 0 m/s.