Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = (6t + et) i + 12t2 j, v(0) = 3i, r(0) = 7 i − 3 j v(t)= r(t)=
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∫a(t) dt = ∫(6t + et)i dt + ∫12t^2 j dt = (3t^2 + et)i + 4t^3 j + C We know that v(0) = 3i, so we can find the constant vector C. When t = 0, v(t) = (3t^2 + et)i + 4t^3 j + C = 3i So, C = 3i Therefore, the velocity vector v(t) = (3t^2 + et)i + 4t^3 j + 3i Show more…
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