Paul's Online Notes
Paul's Online Notes
Home / Calculus II / 3-Dimensional Space / Velocity and Acceleration
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

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