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

AP Calculus ABmediummcq1 pt

A particle moves along the $x$ -axis with velocity $v(t)=t^2-4t+3$ . If its position at $t=0$ is $5$ , what is its position at $t=4$ ?

A.

\frac{11}{3}

B.

\frac{4}{3}

C.

\frac{13}{3}

D.

\frac{19}{3}

Explanation

Core Concept

The change in position is $\int_0^4(t^2-4t+3)\,dt=[\frac{t^3}{3}-2t^2+3t]_0^4=\frac{4}{3}$ . So $s(4)=5+\frac{4}{3}=\frac{19}{3}$ .

Correct Answer

D $\frac{19}{3}$

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