The position vector of a particle is r(t). Find the requested vector.
-$\text { The velocity at } t = 3 \text { for } \mathbf { r } ( t ) = \left( 7 t ^ { 2 } + 4 t + 3 \right) \mathbf { i } - 3 t ^ { 3 } \mathbf { j } + \left( 8 - t ^ { 2 } \right) \mathbf { k }$
A) v(3) = 46i + 81j + 6k
B) v(3) = 25i - 27j - 3k
C) v(3) = 46i - 81j - 6k
D) v(3) = 38i - 81j - 6k

Question

Quizplus · Accepted Answer

The velocity vector can be found by taking the derivative of the position vector with respect to time. Thus, we have:

$\mathbf{v}(t) = \frac{d\mathbf{r}}{dt} = (14t+4)\mathbf{i} -9t^2\mathbf{j} -2t\mathbf{k}$

To find the velocity at $t=3$, we simply substitute $t=3$ into this expression:

$\mathbf{v}(3) = (14(3)+4)\mathbf{i} -9(3)^2\mathbf{j} -2(3)\mathbf{k} = 46\mathbf{i}-81\mathbf{j}-6\mathbf{k}$

Therefore, the answer is C.

The Position Vector of a Particle Is R(t) A) V(3) = 46i + 81j + 6k B) V(3)

The Position Vector of a Particle Is R(t) A) V(3) = 46i + 81j + 6k
B) V(3)