Throwing an object in the air [closed]

Studying formulas about velocity and acceleration I came up with a question: if I throw an object in the air with a velocity $v_0$ (suppose i throw it vertically) in how much time its final velocity $v_f$ will reduce to $0$ due to the force go gravity? Here is how I tried to solve the problem:

Calculation of the time

I know that the final velocity of a object that receive an acceleration is: $$v_f=v_0+at$$ where $a$ is the acceleration and $t$ is the time in which the acceleration acts. I supposed that $v_f$ after a negative acceleration (the gravitational acceleration on Earth $g$) will reduce to $0$ and so I set up the following equation: $$0=\vec{v_0}-\vec{g}\cdot t$$ and solving the equation for $t$ I got that \begin{equation} t=\frac{v_0}{g}\tag{1} \end{equation}

Calculation of the space

I know that the formula to calculate the space that is made by an object moving with an acceleration is $$S=v_0t+\frac12 at^2$$ But now I can apply $(1)$ to the equation: $$S=v_0\cdot \frac{v_0}{g}-\frac12 g\left(\frac{v_0}{g}\right)^2$$ $$S=\frac{v_0^2}{g}-\frac{v_0^2}{2g}=\frac{v_0^2}{2g}\tag{2}$$ That would be the formula for the space.

Reassuming an object thrown in the air with a velocity $v$ will stop moving in the air after a time $t=\frac{v}{g}$ after making a distance $S=\frac{v^2}{2g}$.

Is this correct?

closed as off-topic by ja72, Brandon Enright, Kyle Kanos, David Z♦May 22 '14 at 21:16

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• The time is $t=\frac{v_0}{g}$ and not $t=\frac{v^2}{g}$ you wrote in the end. Also your factor $0.051$ has units that you need to include to make the equation correct. – ja72 May 22 '14 at 20:12
• I corrected the equations. Sorry for the error – Peterix May 22 '14 at 20:31
• Why this question got -1? – Peterix May 22 '14 at 20:36
• It is offtopic. Homework questions are to ask about specific concepts, not to check your results. Here is the policy: meta.physics.stackexchange.com/questions/714/… – Davidmh May 22 '14 at 21:00
• This is NOT a home work question this is a problem that I invented BY MY OWN – Peterix May 23 '14 at 7:07