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M3: velocity as a function of displacement

im very tired so I could be being stupid but how is velocity (v) a function displacement (s)?

I know you differentiate v to get s and integrate s to get v.
Original post by Maths&physics
I know you differentiate v to get s and integrate s to get v.


It's the other way round.
(edited 6 years ago)
Original post by RDKGames
It's the other way round.


according to the tutorial, v = f (s) : v is a function of displacement. what does that mean? btw, ive not slept in over 24 hours - long story, and I dont plan to make a habit out of it.
Original post by Maths&physics
according to the tutorial, v = f (s) : v is a function of displacement. what does that mean? btw, ive not slept in over 24 hours - long story, and I dont plan to make a habit out of it.


Generally, velocity is a function time. But if you can express vv in terms of ss then it can be a function of displacement as well.

For example, if s(t)=e2ts(t)=e^{2t} then v(t)=2e2tv(t)=2e^{2t} hence v(s)=2sv(s) = 2s

It means that if you only know your displacement at some time, but you do not know the time, then you can still determine its velocity at that point, since velocity is only dependent on displacement in such cases.
(edited 6 years ago)
Original post by RDKGames
Generally, velocity is a function time. But if you can express vv in terms of ss then it can be a function of displacement as well.

For example, if s(t)=e2ts(t)=e^{2t} then v(t)=2e2tv(t)=2e^{2t} hence v(s)=2sv(s) = 2s

It means that if you only know your displacement at some time, but you do not know the time, then you can still determine its velocity at that point, since velocity is only dependent on displacement in such cases.


did you differentiate: s(t) to get 2e^2t ???
Original post by Maths&physics
did you differentiate: s(t) to get 2e^2t ???


Yes...

v(t)=ddts(t)v(t) = \dfrac{d}{dt} s(t)
Original post by RDKGames
Yes...

v(t)=ddts(t)v(t) = \dfrac{d}{dt} s(t)


thanks. I think I should go over it tomorrow once ive slept.
Original post by RDKGames
Yes...

v(t)=ddts(t)v(t) = \dfrac{d}{dt} s(t)


ok, I get that but what does dv/ds give you?
(edited 6 years ago)
Original post by Maths&physics
ok, I get that but what does dv/ds give you?


dvds=dvdtdsdt=av\dfrac{dv}{ds} = \dfrac{\frac{dv}{dt}}{\frac{ds}{dt}} = \dfrac{a}{v}

Where s,v,as,v,a are all functions of time.
Original post by RDKGames
dvds=dvdtdsdt=av\dfrac{dv}{ds} = \dfrac{\frac{dv}{dt}}{\frac{ds}{dt}} = \dfrac{a}{v}

Where s,v,as,v,a are all functions of time.


a / v = ?
Original post by Maths&physics
a / v = ?


That's it, I'm not sure what you are looking for
Original post by RDKGames
That's it, I'm not sure what you are looking for


Ok, it doesn’t equal time or displacement?

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