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

A particle of mass m's velocity varies according to bx^{-n}

Find the position as a function of time, setting x = x_{0}at t=0

2. Relevant equations

v(x) = bx^{-n}

possibly relevant: f(x) = -b^{2}mnx^{-2n-1}

3. The attempt at a solution

The first part of the question asked me to find the force acting on the particle as a function of x, which I did using the chain rule. I'm a little unclear as to whether I need f(x) to get x(t).

Anyway, here's my attempt at a solution:

dv/dt = (dv/dx)*(dx/dt)

dv/dt = (dv/dx) * v(x)

Both of these quantities are known so I plugged them in and got an expression for dv/dt. I then tried to integrate that expression twice, once to get v(t) and another time to get x(t). However, when I do that I just get the expression times t^{2}/2, which would make x(0) = 0, not x_{0}as the problem statement gives.

Am I doing this the complete wrong way or am I on the right track and just not understanding calculus?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Advanced mechanics - x(t) from v(x)

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