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Topic 4.9 expresses planar motion with vector-valued functions.

  • Position: parametric f(t) = (x(t), y(t)) becomes p(t) = <x(t), y(t)> or x(t)i + y(t)j (4.9.A.1).
  • Distance: |p(t)| is distance from the origin (4.9.A.1).
  • Velocity: vector-valued v(t) describes motion direction over time (4.9.A.2).
  • Direction: component signs indicate right/left and up/down (4.9.A.2).
  • Speed: |v(t)| is speed at time t (4.9.A.2).

Course scope only (Unit 4 additional topic; not on the AP Exam).

Why It Matters

Vector-valued functions connect parametric motion (4.1-4.3) with vector tools (4.8).

How Families Can Help

  • Write p(t) before computing |p(t)|.
  • Separate position distance from speed |v(t)|.
  • Support direction claims with component signs or table values.

What Not to Do

  • Do not confuse |p(t)| with |v(t)|.
  • Do not skip vector notation when parametric form is given.
  • Do not claim direction without referencing component signs/data.

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

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