The discussion revolves around the integration of Newton's second law, specifically the equation \(\frac{mdv}{F(v)} = dt\), to derive an expression for time \(t\) in terms of velocity \(v\). Participants are exploring the implications of integrating force as a function of velocity and the relationships between velocity, time, and force.
The discussion is active, with participants providing insights on the integration process and clarifying misconceptions about variable usage. Some participants have offered guidance on how to approach the integral and the interpretation of results, while others are still seeking clarity on specific steps and concepts.
Participants are working within the constraints of a homework problem that requires them to integrate and analyze motion under a force dependent on velocity. There is an emphasis on understanding the implications of constant versus variable forces and the correct application of integration techniques.
Oblio said:I thought we subbed F(v) out of the integral?
Oblio said:t =mF(v) \int^{v}_{vo} dv
Oblio said:t= mF(o) \int^{v}_{vo} dv
t= mF(o) (v-vo)
solve for v from here?
Oblio said:Typo. my bad
v = F(o)t / m + V(o) ?
Oblio said:So... why is this especially significant? They want to see some kind of comment.
Something to do with velocity dependence?
Oblio said:the motion would be linear i believe
Oblio said:YES! your back :)
um...
increasing with time?
Oblio said:also constant?
Oblio said:O ya!
I can say both are linear then?