AP®︎ Calculus BC: Topic 8.2 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 8.2 of AP Calculus BC – Connecting Position, Velocity, and Acceleration of Functions Using Integrals.


Questions List

Topic 8.2

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Question 1 Easy

A particle moves along the x-axis, with right positive, with velocity v(t)=6t2+2v(t)=6t^2+2 meters per second for t≥0t\geq 0, where tt is measured in seconds. Its position x(t)x(t) is measured in meters, and x(0)=−4x(0)=-4. What is the particle's position at t=2t=2 seconds?

A2424 meters
B4848 meters
C1616 meters
D2020 meters

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 8.2: Connecting Position, Velocity, and Acceleration of Functions Using Integrals

Learning Objective: CHA-4.C

Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.

Essential Knowledge: CHA-4.C.1

For a particle in rectilinear motion over an interval of time, the definite integral of velocity represents the particle’s displacement over the interval of time, and the definite integral of speed represents the particle’s total distance traveled over the interval of time.