A particle has acceleration

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

Problem

A particle has acceleration a(t)=⟨et,cos⁡t⟩\mathbf a(t)=\langle e^{t},\cos t\rangle. Its velocity at t=0t=0 is v(0)=⟨2,−1⟩\mathbf v(0)=\langle 2,-1\rangle, and its position at t=πt=\pi is r(π)=⟨5,4⟩\mathbf r(\pi)=\langle 5,4\rangle. What is r(0)\mathbf r(0)? (a) ⟨6−eπ+π, 2−π⟩\langle 6-e^{\pi}+\pi,\,2-\pi\rangle (b) ⟨6−eπ−π, 2+π⟩\langle 6-e^{\pi}-\pi,\,2+\pi\rangle (c) ⟨6−eπ, 2⟩\langle 6-e^{\pi},\,2\rangle (d) ⟨6−eπ−π, 6+π⟩\langle 6-e^{\pi}-\pi,\,6+\pi\rangle

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