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Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A particle moving on a line has position p(t)=t3−6t2+12t+5p(t)=t^3-6t^2+12t+5 meters at time tt seconds.
Total: 6 points

(a) Find the average velocity of the particle on the interval 1≤t≤31\le t\le 3. (2 points)

(b) Use the limit definition at t=2t=2 to find the instantaneous velocity p′(2)p'(2). (3 points)

(c) Explain, using units, why your answers to parts (a) and (b) can be different. (1 point)

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