For a particle with acceleration

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

Problem

For a particle with acceleration a(t)=⟨6t,3⟩\mathbf a(t)=\langle 6t,3\rangle, the velocity at time t=2t=2 is v(2)=⟨5,−1⟩\mathbf v(2)=\langle 5,-1\rangle and the position at time t=0t=0 is r(0)=⟨0,4⟩\mathbf r(0)=\langle 0,4\rangle. Find an explicit formula for the position vector r(t)\mathbf r(t).

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