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

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  • Thread starter karush
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If you find velocity to be negative, the particle is moving to the left. In summary, the position of a particle moving along a coordinate line is given by the equation $s(t) = \sqrt{4+4t}$ and the velocity at $t=3$ is $\frac{1}{2} \frac{m}{s}$.
  • #1
karush
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$\tiny{205.o8.14}$
$\textsf{The position of a particle moving along a coordinate line is given }\\$
$\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}

$\textit{think this is ok, but naybe sugestions}$
 
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  • #2
Hi karush,

That looks perfectly fine to me - no suggestions from my end.
 
  • #3
karush said:
$\tiny{205.o8.14}$
$\textsf{The position of a particle moving along a coordinate line is given }\\$
$\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.
 
  • #4
is a vector a related rate?
 
  • #5
karush said:
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.
 

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

1. What does the variable 't' represent in the equation?

't' represents time in the equation. It is the independent variable that is used to calculate the velocity at a specific moment in time.

2. How is velocity calculated when t=3?

Velocity is calculated by dividing the change in position by the change in time, or v = ∆x/∆t. When t=3, the equation should be substituted with the specific value for time to calculate the velocity at that moment.

3. What are the units of the velocity at t=3?

The units of velocity are distance over time, typically represented as meters per second (m/s) or kilometers per hour (km/h). The specific units at t=3 will depend on the units used for distance and time in the equation.

4. Can the velocity at t=3 be negative?

Yes, the velocity at t=3 can be negative if the object is moving in the negative direction or if the displacement is decreasing at that moment in time.

5. What other factors can affect the velocity at t=3?

The velocity at t=3 can be affected by the acceleration of the object, as well as any external forces acting on the object such as friction or air resistance. It can also be affected by any changes in the initial position or velocity of the object.

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