Carroll Chandler
12/07/2023 · Primary School
4. [-/1 Points] DETAILS MY NOTES SCALCET9 13.4.017. Find the position vector of a particle that has the given acceleration and the specified initial velocity and position. Then on your own using a computer, graph the path of the particle. \[ \mathbf{a}(t)=4 t \mathbf{i}+\sin (t) \mathbf{j}+\cos (2 t) \mathbf{k}, \quad \mathbf{v}(0)=\mathbf{i}, \quad \mathbf{r}(0)=\mathbf{j} \] \( \mathbf{r}(t)=\square \)
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The position vector of the particle is \(\mathbf{r}(t) = \left(\frac{2}{3}t^3 + t\right) \mathbf{i} + \left(t - \sin(t) + 1\right) \mathbf{j} + \left(-\frac{1}{4} \cos(2t) + \frac{1}{4}\right) \mathbf{k}\).
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