Homework Help: Different Forms of Newton's 2nd Law

1. Sep 25, 2013

A. Aspart

I’m supposed to prove that if ΣF(v) = -Av^2, where A is a constant, then Δx = m/A * ln (v0/v) by using Newton’s second law in the form ΣF = m dv/dt.

I can solve the problem by using the form ΣF = mv dv/dx; however, it’s specifically stated that I’m not allowed to use the law in that form (since it's the second part of the particular assignment), and therefore I’m stuck.

Can someone please help? I’d appreciate it.

2. Sep 25, 2013

nasu

Well, they don't ask you to find x(t). Just to prove that it's a solution of the second law for this force law.
Find dv/dt directly from the expression for x(v) and plug in.

3. Sep 25, 2013

A. Aspart

Thanks for the reply. I realise now that I misunderstood the assignment.

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