Different Forms of Newton's 2nd Law

[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.

 

[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.

 

[A. Aspart]

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