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Astrophysics
 one year ago
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Astrophysics
 one year ago
@empty

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Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Say dw:1437971434694:dw so for velocity we get, \[v = \frac{ ds }{ dt }\] for a particle moving through the displacement delta s yeee?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0So for acceleration then, say dw:1437971693486:dw we get \[a = \frac{ dv }{ dt }\] (I made pewww pewww noises when I wrote down velocity, I can never be a serious physicist)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0So doing some substitution we get \[a = \frac{ d^2s }{ dt^2 }\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0So now say we have this diagram dw:1437971855435:dw now it's decelerating. We see here \[\Delta v = v'  v\] will be negative so a will also be negative but it says we will get a differential relation involving displacement, velocity, and acceleration along the path may be obtained by eliminating the time differential dt between \[v = \frac{ ds }{ dt }~~~\text{and}~~~a = \frac{ dv }{ dt }\] giving us \[ads=vdv\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437972125677:dw

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0I guess I could've skipped all that and just went to the equations xD

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I just don't really see the ads=vdv part

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Hmmm I guess in one way we could write it as: \(ads = vdv\) we can divide to both sides like this: \[\frac{a}{v} = \frac{dv}{ds}\] \[\frac{\frac{dv}{dt}}{\frac{ds}{dt}} = \frac{dv}{ds}\] Like that?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0No I mean why is it ads = vdv, why is it set up like that? What does it mean

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0I tried getting that expression without going backwards, and I can't lol, like I started with just \[a = \frac{ dv }{ dt }\] and ended up with \[v = \frac{ dv }{ ds }\] but I don't know if this is even right..lol

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Hmmmm I am not entirely sure what your question is, like "why is it this way" or "how does it end up this way" and I think I can only answer the second question haha

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Hehe we can shift the numerators on "dt" to get to the other side of that middle equals sign there kinda haha $$a ds = \frac{dv}{dt}ds = dv\frac{ds}{dt} = dv v$$

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Lol well thanks xD, I see what you're doing, but only I can answer my own question I think because it's probably just something trivial...thanks mang!
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