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Question

# The position vector r describes the path of an object moving in space. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. Position Vector: r(t) = 3ti + tj + ¼t²k Time: t = 2

Solutions

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To evaluate the velocity vector and the acceleration vector

\begin{aligned}\mathbf{v}(t)&=3\mathbf{i}+\mathbf{j}+\frac12t\mathbf{k}, \\ \mathbf{a}(t)&=0\mathbf{i}+0\mathbf{j}+\frac12\mathbf{k},\end{aligned}

of the given object at the given value of $t=2$, we just need to find the value of $\mathbf{v}(2)$ and $\mathbf{a}(2).$

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