For , a particle’s velocity is . For , the velocity is . Given , find the -coordinate…

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

Problem

For 0≤t≤40\le t\le 4, a particle’s velocity is v(t)=⟨t, 2t, 0⟩\mathbf v(t)=\langle t,\,2t,\,0\rangle. For 4<t≤84< t\le 8, the velocity is v(t)=⟨4, 8, t−4⟩\mathbf v(t)=\langle 4,\,8,\,t-4\rangle. Given r(0)=⟨−2, 1, 3⟩\mathbf r(0)=\langle -2,\,1,\,3\rangle, find the zz-coordinate of the particle at t=8t=8. (a) 1919 (b) 1111 (c) 88 (d) 2727

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