Calculus I · Unit 2B · quiz

Interpretation and Motion Concept Quiz

Concept Quiz: Higher Derivatives and Motion

• Distinguish velocity from speed. • Can a particle have zero velocity and nonzero acceleration? • When does a particle change direction? • State the sign test for speeding up. • What does $f"<0$ say about $f'$ ? • Give an example where $f'>0$ and $f"<0$ .

After the explanation

Use the section idea

Reading lens

Use the sign, size, units, and zeros of derivatives to tell a time-aligned story about motion or another changing quantity.

Mental model

Position, velocity, and acceleration are synchronized views: amount, rate of amount, and rate of the rate.

Decision

Separate direction from speed, and compare the signs of velocity and acceleration before describing speeding behavior.

Common trap

Treating negative velocity as slowing down or confusing a function's height with the slope of its graph.

Check yourself

Can you interpret a first and second derivative at the same input without mixing their units or meanings?

Structured concept quiz

Interpretation and Motion Concept Quiz

Write a response before revealing the model. These conceptual items use an honest attempt-and-reveal rubric rather than pretending an open response has one machine-provable wording.

Interactive checkinterpretation-concept-quiz-01

Distinguish velocity from speed.