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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 12.11 : Velocity and Acceleration
- An objects acceleration is given by \(\vec a = \cos \left( {2t} \right)\,\vec i + 4{t^3}\,\vec j + 6\sin \left( {3t} \right)\vec k\). The objects initial velocity is \(\vec v\left( 0 \right) = 6\,\vec i + 2\vec j + 7\vec k\) and the objects initial position is \(\vec r\left( 0 \right) = \vec i - 9\vec j + 6\vec k\). Determine the objects velocity and position functions.
- An objects acceleration is given by \(\vec a = 10t\,\vec i - 6\,\vec j + t\cos \left( t \right)\vec k\). The objects initial velocity is \(\vec v\left( 0 \right) = - \,\vec i + 11\vec j - \vec k\) and the objects initial position is \(\vec r\left( 0 \right) = 4\vec i + \vec j + 10\vec k\). Determine the objects velocity and position functions.
- Determine the tangential and normal components of acceleration for the object whose position is given by \(\vec r\left( t \right) = \left\langle {5t,1 - 2t,4{t^{\frac{3}{2}}}} \right\rangle \).
- Determine the tangential and normal components of acceleration for the object whose position is given by \(\vec r\left( t \right) = \left\langle {6,{{\bf{e}}^{ - 5t}},3t{{\bf{e}}^{ - 5t}}} \right\rangle \).