Tutorial Exercise

Find the velocity, acceleration, and speed of a particle with the given position function.

$r(t)=7\sqrt[\phantom{2}]{2}ti{e}^{7t}j{e}^{-7t}k$

Step $1$

We remember that for a position vector $r(t),$ the velocity vector is given by $v(t)=r^{\text{'}}(t),$ and the acceleration vector is given by $a(t)=v^{\text{'}}(t)=r^{\text{'}}(t).$ Therefore, the velocity vector for $r(t)=7\sqrt[\phantom{2}]{2}ti{e}^{7t}j{e}^{-7t}k$ is given by

$v(t)=r^{\text{'}}(t)=$

$$