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I was given the following problem for a homework assignment:

Given F(x,v) = kvx where k is positive and the velocity is v-nought at x = 0, t = 0, what is x as a function of time?

First I derived v as a function of position:

v = v-nought + kx^2/2m

Then, I derived x as a function of time:

x = Sqrt[2mv-nought/k]tan(t*Sqrt[kv-nought/2m])

My problem with this solution is that x is then undefined for various points in time, plus the fact that it jumps from inifnity to negative infinity when it is undefined.

Now, if this is correct, it can be used as proof that the function as given cannot conform to anything in reality. However, it just may be plain out wrong. If it is wrong, I was wondering if someone might supply me with the correct answer as well as how to go about getting it.

Thank you very much for your time.

Given F(x,v) = kvx where k is positive and the velocity is v-nought at x = 0, t = 0, what is x as a function of time?

First I derived v as a function of position:

v = v-nought + kx^2/2m

Then, I derived x as a function of time:

x = Sqrt[2mv-nought/k]tan(t*Sqrt[kv-nought/2m])

My problem with this solution is that x is then undefined for various points in time, plus the fact that it jumps from inifnity to negative infinity when it is undefined.

Now, if this is correct, it can be used as proof that the function as given cannot conform to anything in reality. However, it just may be plain out wrong. If it is wrong, I was wondering if someone might supply me with the correct answer as well as how to go about getting it.

Thank you very much for your time.

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