$\text { The position vector } \mathbf { r } ( t ) = 4 t \mathbf { i } + 2 t \mathbf { j } + \frac { 1 } { 6 } t ^ { 2 } \mathbf { k } \text { describes the path of an object moving in }$ space. Find the acceleration $\mathbf { a } ( t )$ of the object.
A) $\mathbf { a } ( t ) = \frac { 1 } { 6 } \mathbf { k }$
B) $\mathbf { a } ( t ) = 4 \mathbf { i } + 2 \mathbf { j }$
C)$\mathbf { a } ( t ) = 4 \mathbf { i } + 2 \mathbf { j } + \frac { 1 } { 3 } \mathbf { k }$
D) $\mathbf { a } ( t ) = 4 \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k }$
E) $\mathbf { a } ( t ) = \frac { 1 } { 3 } \mathbf { k }$

Question

Quizplus · Accepted Answer

Acceleration $\mathbf{a}(t)$ is the second derivative of the position vector $\mathbf{r}(t)$ with respect to time $t$. The components $4t\mathbf{i} + 2t\mathbf{j}$ have zero second derivatives, and the second derivative of $\frac{1}{6}t^2\mathbf{k}$ is $\frac{1}{3}\mathbf{k}$.

Space Find the Acceleration a(t)\mathbf { a } ( t )a(t)

Space Find the Acceleration $\mathbf { a } ( t )$