Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 6t j + 12t2 k, v(0) = i, r(0) = 6 j − 4 k v(t) = r(t) =
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Step 1: Find the velocity vector \( \mathbf{v}(t) \) using the given acceleration vector \( \mathbf{a}(t) \): Integrate the acceleration vector \( \mathbf{a}(t) = 2\mathbf{i} + 6t\mathbf{j} + 12t^2\mathbf{k} \) with respect to \( t \) to get the velocity vector: \[ Show more…
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