My Math Forum Trivial problem to obtain Distance from Velocity.

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 January 7th, 2014, 03:05 AM #1 Senior Member   Joined: Jan 2013 From: Italy Posts: 154 Thanks: 7 Trivial problem to obtain Distance from Velocity. Hi, i don't know if this is the right place to post this but, I want to know if i'm done right about this very trivial physic problem. Can you help me please? I wasn't so good about physics in high school, so now i'm trying to do physics in a rational way because I want to comprehend every passage that brings to obtain a particular formula. I have this basic problem: A train travels away at a velocity $v$ mph (miles per hour). At $t=0$ it is distance $S_0$ from us. Write the equation for the distance the train is from us $S$ in terms of time $t$. So: reading this problem I can understand that we know the velocity, and that is $v$. By definition, the velocity is the distance traveled divided by the time. So in a plot with space in function of time, this velocity, is the slope of the line in that one. Reading the problem, I don't know anything about the distance formula, so I want to obtain that from the velocity, that I call $v$, and, by definition, it is the ratio of $S$ to $t$: $v= \frac{S - S_0}{t-t_0}$ we know that $t_0= 0$ so: $v= \frac{S - S_0}{t}$ from this last equation I can obtain the distance: $v= \frac{S}{t} - \frac{S_0}{t}$ $\frac{S}{t}= \frac{S_0}{t} + v$ $\frac{S}{t} \cdot t= (\frac{S_0}{t} + v) \cdot t$ $S= \frac{S_0}{t}\cdot t + v \cdot t$ $S= S_0 + vt$ this last equation I obtained is the equation of the distance. I think that this is the right way to follow to obtain it. is it right? many thanks for your patience!
 January 7th, 2014, 11:58 AM #2 Global Moderator   Joined: May 2007 Posts: 6,754 Thanks: 695 Re: Trivial problem to obtain Distance from Velocity. It will be a lot quicker and clearer if you multiply through by t right after the second line to get: vt = S - So. Therefore S = So + vt.

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