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### Section 12.11 : Velocity and Acceleration

1. An objects acceleration is given by $$\vec a = 3t\,\vec i - 4{{\bf{e}}^{ - t}}\,\vec j + 12{t^2}\vec k$$. The objects initial velocity is $$\vec v\left( 0 \right) = \vec j - 3\vec k$$ and the objects initial position is $$\vec r\left( 0 \right) = - 5\vec i + 2\vec j - 3\vec k$$. Determine the objects velocity and position functions. Solution
2. Determine the tangential and normal components of acceleration for the object whose position is given by $$\vec r\left( t \right) = \left\langle {\cos \left( {2t} \right), - \sin \left( {2t} \right),4t} \right\rangle$$. Solution