Mathematics

Mathematics

Problem

A particle has acceleration a(t)=⟨cos⁡t,−sin⁡t⟩\mathbf a(t)=\langle \cos t,-\sin t\rangle. Given that v(0)=⟨0,1⟩\mathbf v(0)=\langle 0,1\rangle and r(π)=⟨4,0⟩\mathbf r(\pi)=\langle 4,0\rangle, determine the position vector r(0)\mathbf r(0).

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