Derivatives and motion

Position, velocity, and acceleration, and reading when a particle speeds up or changes direction.

Standards:AP Calc AB · Unit 4

Try it: three questions

Real questions from the practice bank. Tap an answer to check it.

Question 1 of 3

A particle moves along a straight line with position function s(t) = 3t³ − 12t² + 9t, where s is in meters and t is in seconds. Find the acceleration when t = 2.

Question 2 of 3

A particle moves along a straight line with position function s(t) = t³ − 6t² + 9t, where s is in meters and t is in seconds. What is the acceleration of the particle at t = 2 seconds?

Question 3 of 3

A particle moves along a line with position function s(t) = 2t³ − 9t² + 12t, where s is in metres and t is in seconds. Find the acceleration of the particle at t = 2 seconds.

How this fits in

Derivatives and motion is one skill in the Intro to Calculus unit. Students read the unit lesson, then earn a bronze, silver, or gold medal on their last 10 answers. Medals never go down. A mastered unit comes back for review after 1, 3, 7, 16, and 35 days so it stays learned.

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