MHB 205.o8.14} what is the velocity when t=3

[karush]

$\tiny{205.o8.14}$
$\textsf{The position of a particle moving along a coordinate line is given }\\$
$\textsf{what is the velocity when $t=3$}\\$

\begin{align}
\displaystyle
{s(t)}&={\sqrt{4+4t}}\\
&=2(1+t)^{1/2}\\
s'(t)&=\frac{1}{\sqrt{1+t}}\\
s'(3)&=\color{red}{\frac{1}{2}\frac{m}{s}}
\end{align}

$\textit{think this is ok, but naybe sugestions}$

 

[Dethrone]

Hi karush,

That looks perfectly fine to me - no suggestions from my end.

 

[IanCg]

$\tiny{205.o8.14}$
$\textsf{The position of a particle moving along a coordinate line is given }\\$
$\textsf{what is the velocity when $t=3$}\\$

\begin{align}
\displaystyle
{s(t)}&={\sqrt{4+4t}}\\
&=2(1+t)^{1/2}\\
s'(t)&=\frac{1}{\sqrt{1+t}}\\
s'(3)&=\color{red}{\frac{1}{2}\frac{m}{s}}
\end{align}

$\textit{think this is ok, but naybe sugestions}$

I think the value you have found is the speed. If the question really means velocity then your answer should be a vector.

 

[karush]

is a vector a related rate?

 

[MarkFL]

is a vector a related rate?

Velocity in 1 dimension can "point" in only 1 of 2 directions, which is indicated by the sign. Since you find the requested velocity to be positive, you know the particle is moving to the right.