Velocity-Based Differentiation for B(s) in a Simple Homework Problem

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The discussion revolves around finding the rate of change of B(s) in terms of velocity rather than displacement. The user initially expresses B(s) as proportional to 1/s^3 and seeks to relate the derivative B'(s) to velocity. After some back-and-forth, it is confirmed that the velocity is constant, and the user ultimately arrives at a solution expressing the rate of change as B proportional to -3/s^3 multiplied by dv/dt. The conversation highlights the importance of understanding the relationship between displacement and velocity in the context of differentiation. The problem is resolved with the user finding a satisfactory expression for B(s).
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Homework Statement



I have nearly finished a problem. I am at the stage where I have:

B(s)\propto\frac{1}{s^{3}}

v=\frac{ds}{dt}

I want to find the rate of change of B(s), but expressed in terms of a velocity, rather than a displacement.

Homework Equations



So for displacement:

B'(s) \propto\frac{-3}{s^{2}}

The Attempt at a Solution


How can I express this in terms of v instead? My guess would be that:

B'(s) \propto\frac{1}{v^{3}}

but I'm not sure that's correct. This does seem like quite a simple problem but its really got me stumped.

Thanks in advance, Ewan
 
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Is the velocity constant?
Do you mean by rate of change

\frac{dB(s)}{dt}?
And I think it would be better if you post whole question.
 
Last edited:
azatkgz said:
Is the velocity constant?
Do you mean by rate of change

\frac{dB(s)}{dt}?
And I think it would be better if you post whole question.

Yes the velocity is constant. The rest of the question isn't relevant to my problem, but I can post if you want. And yes by rate of change I mean:

\frac{dB(s)}{dt}
 
Last edited:
Can you post?
 
Never mind I managed to solve it (i think!).

B \propto \frac{-3}{s^{3}} \frac{dv}{dt}

using substitution of s for v.
 
Last edited:
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