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Motion in One Dimension: Displacement, Velocity, Acceleration

Learn the fundamentals of motion in one dimension, covering concepts like displacement, velocity, acceleration, and integration. Explore how to analyze graphs and equations, understand derivatives, and solve integration problems.

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Motion in One Dimension: Displacement, Velocity, Acceleration

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  1. 2 Motion in One Dimension • Displacement, velocity, speed • Acceleration • Motion with Constant Acceleration • Integration • Hk: 13, 27, 51, 59, 69, 81, 83, 103.

  2. Terminology • “delta” = change • “o” = initial • “ ” = final • Position • Displacement • Speed • Velocity • Acceleration

  3. Concepts • Slope & derivative (Giam 12-13) • Average vs instantaneous (Giam 12-13) • Integration & area under curve (Tipler) • Acceleration/force, velocity/force • Graph shapes & equations (Giam 21)

  4. Derivative Equation • Constant acceleration (constant force) • Take derivative

  5. Derivative Equation

  6. Integrated Equations • Integrate “a” with time

  7. Integrated Equations

  8. V-squared Equation • Integrate “a” over distance “x”

  9. V-squared Equation

  10. Average Velocity with Uniform Acceleration Uniform Acceleration = constant valued acceleration During uniform acceleration, average velocity is halfway between vo and v: 10

  11. Summary • Speed = rate of travel • Velocity = speed & direction • Acceleration = rate of velocity change • Motion with Constant Acceleration • Integration

  12. Problems • Describe motion (tipler 49)

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