$\text { The position vector } \mathbf { r } ( t ) = \left\langle 2 \cos t , 4 \sin t , t ^ { 2 } \right\rangle \text { describes the path of an object moving }$ in space. Find the velocity $\mathbf { v } ( t )$ of the object.
A) $\mathbf { v } ( t ) = 2 \sin t \mathbf { i } - 4 \cos t \mathbf { j } + \mathbf { k }$
B) $\mathbf { v } ( t ) = - 2 \cos t \mathbf { i } - 4 \sin t \mathbf { j } + 2 \mathbf { k }$
C) $\mathbf { v } ( t ) = - 2 \sin t \mathbf { i } - 4 \cos t \mathbf { j } + \mathbf { k }$
D) $\mathbf { v } ( t ) = - 2 \sin t \mathbf { i } + 4 \cos t \mathbf { j } + 2 t \mathbf { k }$
E) $\mathbf { v } ( t ) = - 2 \cos t \mathbf { i } + 4 \sin t \mathbf { j } + \mathbf { k }$

Question

Quizplus · Accepted Answer

The velocity vector $\mathbf{v}(t)$ is found by differentiating the position vector $\mathbf{r}(t)$ with respect to $t$. Differentiating each component of $\mathbf{r}(t) = \langle 2\cos t, 4\sin t, t^2 \rangle$ gives $\mathbf{v}(t) = \langle -2\sin t, 4\cos t, 2t \rangle$.

In Space Find the Velocity v(t)\mathbf { v } ( t )v(t)

In Space Find the Velocity $\mathbf { v } ( t )$