Mr. Lowrie's Science Site
  • Home
  • Environmental Systems
    • First Week Stuff
    • Key Terms Glossary
    • Unit 1: Introduction to Environmental Science >
      • Chapter 1: Science and the Environment >
        • Section 1: Understanding Our Environment
        • Section 2: The Environment and Society
      • Chapter 2: Tools of Environmental Science >
        • Section 1: Scientific Methods
        • Section 2: Statistics and Models
        • Section 3: Making Informed Decisions
      • Chapter 3: The Dynamic Earth >
        • Section 1: The Geosphere
        • Section 2: The Atmosphere
        • Section 3: The Hydrosphere and Biosphere
    • Unit 2: Ecology >
      • Chapter 4: The Organization of Life >
        • Section 1: Ecosystems: Everything is Connected
        • Section 2: Evolution
        • Section 3: The Diversity of Living Things
      • Chapter 5: How Ecosystems Work >
        • Section 1: Energy Flow in Ecosystems
        • Section 2: The Cycling of Materials
        • Section 3: How Ecosystems Change
      • Chapter 6: Biomes >
        • Section 1: What is a Biome?
        • Section 2: Forest Biomes
        • Section 3: Grassland, Desert, and Tundra Biomes
      • Chapter 7: Aquatic Ecosystems >
        • Section 1: Freshwater Ecosystems
        • Section 2: Marine Ecosystems
    • Unit 3: Populations >
      • Chapter 8: Understanding Populations >
        • Section 1: How Populations Change in Size
        • Section 2: How Species Interact with Each Other
      • Chapter 9: The Human Population >
        • Section 1: Studying Human Populations
        • Section 2: Changing Population Trends
      • Chapter 10: Biodiversity >
        • Section 1: What is Biodiversity?
        • Section 2: Biodiversity at Risk
        • Section 3: The Future of Biodiversity
    • Unit 4: Water, Air, and Land >
      • Chapter 11: Water >
        • Section 1: Water Resources
        • Section 2: Water Use and Management
        • Section 3: Water Pollution
      • Chapter 12: Air >
        • Section 1: What Causes Air Pollution?
        • Section 2: Air, Noise, and Light Pollution
        • Section 3: Acid Precipitation
      • Chapter 13: Atmosphere and Climate Change >
        • Section 1: Climate and Climate Change
        • Section 2: The Ozone Shield
        • Section 3: Global Warming
      • Chapter 14: Land >
        • Section 1: How We Use Land
        • Section 2: Urban Land Use
        • Section 3: Land Management and Conservation
      • Chapter 15: Food and Agriculture >
        • Section 1: Feeding the World
        • Section 2: Crops and Soil
        • Section 3: Animals and Agriculture
    • Unit 5: Mineral and Energy Resources >
      • Chapter 16: Mining and Mineral Resources >
        • Section 1: Minerals and Mineral Resources
        • Section 2: Mineral Exploration and Mining
        • Section 3: Mining Regulations and Mine Reclamation
      • Chapter 17: Nonrenewable Energy >
        • Section 1: Energy Resources and Fossil Fuels
        • Section 2: Nuclear Energy
      • Chapter 18: Renewable Energy >
        • Section 1: Renewable Energy Today
        • Section 2: Alternative Energy and Conservation
      • Chapter 19: Waste >
        • Section 1: Solid Waste
        • Section 2: Reducing Solid Waste
        • Section 3: Hazardous Wastes
    • Unit 6: Our Health and Future >
      • Chapter 20: The Environment and Human Health >
        • Section 1: Pollution and Human Health
        • Section 2: Biological Hazards
      • Chapter 21: Economics, Policy, and the Future >
        • Section 1: Economics and International Cooperation
        • Section 2: Environmental Policies in the United States
        • Section 3: The Importance of the Individual
  • AP Environmental Science
    • First Week Stuff
    • Unit I: Humans and Sustainability: An Overview >
      • Chapter 1: Environmental Problems, Their Causes, and Sustainability
    • Unit II: Science, Ecological Principles, and Sustainability >
      • Chapter 2: Science, Matter, Energy, and Systems
      • Chapter 3: Ecosystems: What are They and How Do They Work?
      • Chapter 4: Biodiversity and Evolution
      • Chapter 5: Biodiversity, Species Interactions, and Population Control
      • Chapter 6: The Human Population and Its Impact
      • Chapter 7: Climate and Biodiversity
      • Chapter 8: Aquatic Biodiversity
    • Unit III: Sustaining Biodiversity >
      • Chapter 9: Sustaining Biodiversity: Saving Species and Ecosystem Services
      • Chapter 10: Sustaining Terrestrial Biodiversity: Saving Ecosystems and Ecosystem Services
      • Chapter 11: Sustaining Aquatic Biodiversity and Ecosystem Services
    • Unit IV: Sustaining Natural Resources >
      • Chapter 12: Food Production and the Environment
      • Chapter 13: Water Resources
      • Chapter 14: Nonrenewable Mineral Resources
      • Chapter 15: Nonrenewable Energy
      • Chapter 16: Energy Efficiency and Renewable Energy
    • Unit V: Sustaining Environmental Quality >
      • Chapter 17: Environmental Hazards and Human Health
      • Chapter 18: Air Pollution
      • Chapter 19: Climate Disruption
      • Chapter 20: Water Pollution
      • Chapter 21: Solid and Hazardous Waste
      • Chapter 22: Urbanization and Sustainability
    • Unit VI: Sustaining Human Societies >
      • Chapter 23: Economics, Environment, and Sustainability
      • Chapter 24: Politics, Environment, and Sustainability
      • Chapter 25: Environmental Worldviews, Ethics, and Sustainability
  • Chemistry
    • First Week Stuff
    • Matter

Motion Along a Straight Line


Position:  The position (x) of a particle on an x axis locates the particle with respect to the origin, or zero point, of the axis.  The position is either positive or negative, according to which side of the origin the particle is on, or zero if the particle is at the origin.  The positive direction on an axis is the direction of increasing positive numbers;  the opposite direction is the negative direction on the axis.

Displacement:  The displacement (delta x) of a particle is the change in its position:
Picture
Displacement is a vector quantity.  It is positive if the particle has moved in the positive direction of the x axis and negative if the particle has moved in the negative direction.

Average velocity:  When a particle has move from position x1 to position x2 during a time interval delta t = t2 - t1, its average velocity during that interval is:
Picture
The algebraic sign of v-avg indicates the direction of motion (v-avg is a vector quantity).  Average velocity does not depend on the actual distance a particle moves, but instead depends on its original and final positions.
-On a graph of x versus t, the average velocity for a time interval delta t is the slope of the straight line connecting the points on the curve that represent the two ends of the interval.

Average speed:  The average speed (s) of a particle during a time interval delta t depends on the total distance the particle moves in that time interval:
Picture

Instantaneous Velocity:  The instantaneous velocity (or simply velocity) v of a moving particle is:
Picture
(continued from previous column) where delta x and delta t are defined in the average velocity equation.  The instantaneous velocity (at a particular time) may be found as the slope (at that particular time) of the graph of x versus t.  Speed is the magnitude of instantaneous velocity.

Average acceleration:  Average acceleration is the ratio of a change in velocity (delta v) to the time interval delta t in which the change occurs:
Picture
The algebraic sign indicated the direction of a-avg.

Instantaneous Acceleration:  Instantaneous acceleration (or simply acceleration) a is the first time derivative of velocity v(t) and the second time derivative of position x(t):
Picture
On a graph of v versus t, the acceleration (a) at any time (t) is the slope of the curve at the point that represents t.

Constant acceleration:  The five major kinematics equations in physics describe the motion of a particle with constant acceleration:
Picture
These are not valid when the acceleration is not constant.

Free-Fall Acceleration:  An important example of straight-line motion with constant acceleration is that of an object rising or falling freely near Earth's surface.  The constant acceleration equations describe this motion, but we make two changes in notation:  (1) we refer the motion to the vertical y axis with +y vertically up; (2) we replace a with -g, where g is the magnitude of the free-fall acceleration.  Near Earth's surface, g = 9.8m/s2 (=32ft/s2)

Files:
APCM Chapter 2 Presentation
File Size: 3034 kb
File Type: ppt
Download File


Skills Needed:
  • Dimensional Analysis (Algebra)
  • Equation Manipulation (Algebra)
  • ​Unit Logic
  • Knowledge of Limits (Calculus)
  • Ability to Differentiate (Calculus)
  • Ability to Integrate (Calculus)
  • Equation Memorization

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