(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If we know F(t) the force as a function of time for straight line motion, Newton's second law gives us a(t) the acceleration as a function of time. We can then integrate a(t) to find v(t) and x(t). However, suppose we know F(v) instead. a) The net force on a body moving along the x-axis equals -Cv[itex]^{2}[/itex]. Use Newton's second law written as ƩF = m [itex]\stackrel{dv}{dt}[/itex] and two integrations to show that x - x0 = (m/C) ln(v0/v). b) Show that Newton's second law can be written as ƩF = m*v*[itex]\stackrel{dv}{dx}[/itex]. Derive the same expression in part (a) using this form of the second law and one integration.

2. Relevant equations

F = ma

F(v) = -Cv^2

3. The attempt at a solution

For the first part a), I had no idea so I started to differentiate the answer to try and get a method for simplifying it originally. The problem I encounter is that at X, If I take the 2nd derivative of the function I get a(t) = m/Cv^2, which seems impossible because you cant do that with -Cv^2 = m dv/dt. I solved that for dv/dt but i get nowhere really. I'm extremely stumped. Any pointers in the right direction would be extremely useful.

Thanks in advance.

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# Proving a complex Force derivation with CalcConfused

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