Two particles move in the plane for seconds

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Two particles move in the plane for

0\le t\le\pi

seconds. Particle A has velocity

\mathbf v_{A}(t)=\langle\cos t,\sin t\rangle

m/s, and particle B has velocity

\mathbf v_{B}(t)=\langle 2,0\rangle

m/s. Which of the following correctly states the total distance traveled by each particle on this interval? (a) Particle A travels

2\text{ m}

, and particle B travels

2\pi\text{ m}

. (b) Particle A travels

\pi\text{ m}

, and particle B travels

2\pi\text{ m}

. (c) Particle A travels

2\pi\text{ m}

, and particle B travels

2\pi\text{ m}

. (d) Particle A travels

\pi\text{ m}

, and particle B travels

\pi\text{ m}