Apentix/AP Calculus AB/Unit 8: Applications of Integration/Question

AP Calculus ABmediummcq1 pt

A particle moves along a line with velocity $v(t)=4-t^2$ for $0\le t\le 4$ . What is the total distance traveled by the particle?

A.

-\frac{16}{3}

B.

\frac{16}{3}

C.

16

D.

\frac{32}{3}

Explanation

Core Concept

The velocity changes sign at $t=2$ . The distance is $\int_0^2(4-t^2)\,dt+\int_2^4(t^2-4)\,dt=\frac{16}{3}+\frac{32}{3}=16$ .

Correct Answer

C $16$

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