A particle moves in the plane with acceleration

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

Problem

A particle moves in the plane with acceleration a(t)=⟨2t,−et⟩\mathbf a(t)=\langle 2t,-e^{t}\rangle. Its velocity and position at time t=0t=0 are v(0)=⟨1,0⟩\mathbf v(0)=\langle 1,0\rangle and r(0)=⟨2,−3⟩\mathbf r(0)=\langle 2,-3\rangle, respectively. Determine the particle’s position vector at time t=2t=2.

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