Skip to main content Contents Prev Up Next \(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
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\)
Section 10.6 Motion in Space
The vector version of a parametric curve is given by interpreting \(\rr=\rr(u)\) as the position vector of an object moving along the curve. The derivatives of position are velocity \(\vv\) and acceleration \(\aa\text{:}\)
\begin{align*}
\vv \amp= {d\rr\over du} ,\\
\aa \amp= {d\vv\over du} = {d^2\rr\over du^2} ,
\end{align*}
and speed is the magnitude of velocity:
\begin{equation}
v = |\vv| = \left| {d\rr\over du} \right| .\tag{10.6.1}
\end{equation}
This terminology is most appropriate when the parameter is time, usually denoted by \(t\) instead of \(u\text{.}\)
