The position of a particle is

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

Problem

The position of a particle is r(t)=⟨3sin⁡t, 2t2, cos⁡t⟩\mathbf r(t)=\langle 3\sin t,\, 2t^{2},\, \cos t\rangle. Determine the velocity vector at time t=π2t=\dfrac{\pi}{2}. (a) ⟨0, π, −1⟩\langle 0,\,\pi,\,-1\rangle (b) ⟨0, 2π, −1⟩\langle 0,\,2\pi,\,-1\rangle (c) ⟨0, 2π, 1⟩\langle 0,\,2\pi,\,1\rangle (d) ⟨3, 2π, −1⟩\langle 3,\,2\pi,\,-1\rangle

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