9
QuizMultiple Choice

Unit Test — Unit test

Question 9 • AP Calculus AB - MA5186 A

This question is designed to be answered without a calculator.A particle travels along the x-axis so that its position, in centimeters, after t seconds is given by the function x(t) = –4t3 – 8t2 + 16t – 64. What is the acceleration of the particle at time t = 1 sec?

Answer
A
–52 cm/sec2
B
–40 cm/sec2
C
–24 cm/sec2
D
–12 cm/sec2

Explanation

Acceleration is the second derivative of position. Differentiating x(t) = –4t³ – 8t² + 16t – 64 twice gives a(t) = –24t – 16. At t = 1, a(1) = –24 – 16 = –40 cm/sec², so the correct choice is –40 cm/sec².

AI-written and checked against the verified answer.

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