The velocity of a particle is

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

Problem

The velocity of a particle is v(t)=⟨sin⁡t,0,et⟩\mathbf v(t)=\langle \sin t,0,e^{t}\rangle. If the particle’s position at t=0t=0 is r(0)=⟨0,1,2⟩\mathbf r(0)=\langle 0,1,2\rangle, evaluate the position vector r(2)\mathbf r(2).

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