For , a particle moves with velocity . At time its position is . Derive an explicit…

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

Problem

For t>0t>0, a particle moves with velocity v(t)=t2i+ln⁡(t) j+4cos⁡t k\mathbf v(t)=t^{2}\mathbf i+\ln(t)\,\mathbf j+4\cos t\,\mathbf k. At time t=1t=1 its position is r(1)=⟨2,0,5⟩\mathbf r(1)=\langle 2,0,5\rangle. Derive an explicit expression for r(t)\mathbf r(t).

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