Suppose the position of a particle in motion at time $t$ is given by the vector parametric equation $\vec{r}(t)=\langle 2(t$
(a) Find the velocity of the particle at time $t$.
$$
\vec{v}(t)=
$$
$\square$
(b) Find the speed of the particle at time $t$.

Speed $=$ $\square$
(c) Find the time(s) when the particle is stationary. If there is more than one correct answer, enter your ansh
$$
t=
$$
$\square$

Note: You can earn partial credit on this problem.

Question

Suppose the position of a particle in motion at time $t$ is given by the vector parametric equation $\vec{r}(t)=\langle 2(t$
(a) Find the velocity of the particle at time $t$.
$$
\vec{v}(t)=
$$
$\square$
(b) Find the speed of the particle at time $t$.

Speed $=$ $\square$
(c) Find the time(s) when the particle is stationary. If there is more than one correct answer, enter your ansh
$$
t=
$$
$\square$

Note: You can earn partial credit on this problem.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the velocity of the particle at time $ t $, we differentiate the position vector $ \vec{r}(t) = \langle 2(t), \ldots \rangle $ with respect to $ t $. ‖ ‖ step 2 ⋮ The velocity vector is given by $ \vec{v}(t) = \frac{d\vec{r}}{dt} $. ‖ ‖ step 3 ⋮ The speed of the particle is the magnitude of the velocity vector, calculated as $ \text{Speed} = \|\vec{v}(t)\| $. ‖ ‖ step 4 ⋮ The particle is stationary when $ \vec{v}(t) = \vec{0} $, which we find by solving the equation $ \vec{v}(t) = 0 $. ‖ ∻Answer∻ ⚹ Velocity: $ \vec{v}(t) = \langle \ldots \rangle $, Speed: $ \|\vec{v}(t)\| $, Stationary times: $ t = \ldots $ ⚹ ∻Key Concept∻ ⚹ The velocity and speed of a particle describe its motion in terms of direction and magnitude, respectively. ⚹ ∻Explanation∻ ⚹ The velocity vector is derived from the position vector, and the speed is the magnitude of this velocity. A particle is stationary when its velocity is zero. ⚹◊What is the formula for calculating the curvature of a curve represented by a vector function?⍭ Generate me a similar question◊

Sia