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Motion Along a Line: Position, Displacement, Speed, Velocity, and Acceleration

This chapter discusses the concepts of position, displacement, speed, velocity, and acceleration in one-dimensional motion. It also covers the kinematic equations and free fall acceleration. Various applications and graphs are explored as well.

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Motion Along a Line: Position, Displacement, Speed, Velocity, and Acceleration

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  1. Chapter 2: Motion Along a Line • Position & Displacement • Speed & Velocity • Acceleration • Describing motion in 1D • Free Fall • CQ: 1, 2, 3, 4. • P:1, 11, 13, 25, 27, 29, 47, 50.

  2. Applications • Destination times • Design packing materials & road barriers • Airbag deployment speed • Simulations (movies & games)

  3. Speed • Speed = rate of travel at a given moment of time • Distance traveled = total length of the curved path

  4. Initial/Final Notation Same rules apply for all variables

  5. Delta Notation called Displacement

  6. Velocity (m/s) When Dt is small, Dx/Dt is the instantaneousvelocity v.

  7. Graphs • Wilson (12) x vs t • Giambattist (21) +, -, 0 accel. • area under v vs. t curve = displacement

  8. Acceleration (m/s/s) If Dt is small, Dv/Dt is called the instantaneousacceleration and labeled “a”.

  9. 0 Ex. Car Acceleration from 10m/s to 15m/s in a time of 2.0 seconds. In this class we only use average acceleration and often drop the “avg” notation from acceleration.

  10. Velocity Formula

  11. acceleration • Wilson (15) negative acceleration

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

  13. Average Velocity Formula

  14. Displacement Formula

  15. V-squared Equation

  16. 0 Kinematic Equations with Constant Acceleration

  17. Ex. Human Acceleration In the 1988 Olympics, Carl Lewis reached the 20m mark in 2.96s (Bolt: 2.87s)

  18. 0 Ex: V2 Equation Approximate Stopping Accelerations in m/s/s: Dry Road: ~ 9 (anti-lock) ~ 7 (skidding) Wet Road: ~ 4 (anti-lock) ~ 2 (skidding) At 60mph = 27m/s, what is the skid-to-stop distance on a wet road?

  19. Scalars & Vectors • Scalar: size only • e.g. speed, distance, time • Vector: magnitude and direction • e.g. displacement, velocity, acceleration • In one-dimension the direction is determined by the + or – sign. • In two-dimensions, two numbers are required.

  20. 0 Motion Diagrams • Are velocity-position diagrams • More visual than a graph of x or v vs. time • Arrow gives direction, length represents the speed (use a dot for zero speed) • (net) force required to change velocity • Example: car speeding up to left

  21. Free-Fall Acceleration • a = 9.8m/s/s in downward direction • Ex. Speed of object dropped from rest after 1.0, 2.0, 3.0 seconds: • v = vo + at • v(1.0s) = 0 + (-9.8)(1.0) = -9.8m/s • v(2.0s) = 0 + (-9.8)(2.0) = -19.6m/s • v(3.0s) = 0 + (-9.8)(3.0) = -29.4m/s /

  22. Activities • Moving Man phet animae • Textbook type problems

  23. Summary: • speed: rate of travel • average speed: distance traveled/time. • displacement: change in position • velocity: rate position changes • acceleration: rate velocity changes • kinematic equation set • free fall: constant acceleration. • graphs and slopes

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