A particle moves in space with velocity

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

Problem

A particle moves in space with velocity v(t)=⟨6t, 3, 2t2⟩\mathbf v(t)=\langle 6t,\,3,\,2t^2\rangle. Its position at time t=0t=0 is r(0)=⟨1, −4, 5⟩\mathbf r(0)=\langle 1,\,-4,\,5\rangle. Determine r(2)\mathbf r(2). (a) ⟨13, 2, 21⟩\langle 13,\,2,\,21\rangle (b) ⟨13, 2, 13⟩\langle 13,\,2,\,13\rangle (c) ⟨13, 2, 313⟩\langle 13,\,2,\,\dfrac{31}{3}\rangle (d) ⟨25, 2, 21⟩\langle 25,\,2,\,21\rangle

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