$\text { The position vector } \mathbf { r } ( t ) = 8 t \mathbf { i } + + 4 t \mathbf { j } + 5 t \mathbf { k } \text { describes the path of an object moving in }$ space. Find the speed $s ( t )$ of the object.
A) $s ( t ) = 1 / 73$
B) $s ( t ) = 105$
C) $s ( t ) = 1 / 105$
D) $s ( t ) = 1 / 85$
E) $s ( t ) = 17$

Question

Quizplus · Accepted Answer

The speed is the magnitude of the velocity vector, which is the derivative of the position vector. So,$$s(t) = \left\Vert \frac{d\mathbf{r}}{dt} \right\Vert = \left\Vert 8\mathbf{i} + 4\mathbf{j} + 5\mathbf{k} \right\Vert = \sqrt{8^2 + 4^2 + 5^2} = \sqrt{105} = \frac{1}{\sqrt{105}}.$$

Space Find the Speed s(t)s ( t )s(t) Of the Object

Space Find the Speed $s ( t )$ Of the Object