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Common Mistakes

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Frequent Errors

1. Confusing position vector p(t) with velocity vector v(t) (4.9.A.1 vs 4.9.A.2). 2. Using |p(t)| as speed instead of |v(t)| (4.9.A.2). 3. Omitting vector notation for parametric motion (4.9.A.1). 4. Claiming direction without component sign evidence (4.9.A.2, 3.C). 5. Computing magnitude with arithmetic errors on components (4.8.A.3 link). 6. Treating x(t) and y(t) as scalars unrelated to vectors. 7. Wrong time t substituted into p(t) or v(t). 8. Unsupported speed comparison without |v(t)| values (3.C).

Why These Happen

Students merge parametric, vector, and magnitude ideas too quickly.

How to Fix Them

  • Label p(t) vs v(t) before any magnitude.
  • Build a small table of components and magnitudes.
  • Support each direction/speed claim with numbers.

Avoidance Scripts

  • "Position first, speed second."
  • "Distance from origin: |p(t)|."
  • "Show the component signs."

Quick Self-Check

  • Did I use |p(t)| for distance and |v(t)| for speed?
  • Did I support direction with data?
  • Are parametric and vector forms aligned?

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