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

Hi, I've got an assignment which involves finding the function of velocity against time, given the information that the particle is moving with intial velocity of v_{0}and that it experience a resistive force of -βv^{2}

2. Relevant equations

From the problem I've derived model of: ma = -βv^{2}

3. The attempt at a solution

re-arranging the model, I have equation of:

dv/dt = -β/m * v^{2}

then, using techniques from seperable equation,

dv/v^{2}= -β/m * dt

-1/v = -β/m * t + C_{1}

pluging in v(0) = v_{0}

-1/v_{0}= -β/m * 0 + C_{1}

Or

C_{1}= -1/v_{0}

Now, plugging in C and rearraging the equation, I obtained

-1/v = -β/m * t - 1/v_{0}

v = m/(β * t) + v_{0}

So as you can see, I'm able to derived the velocity function, but the problem lies to the fact that if I try to plug in t=0 for the velocity, then the function will not work as division by zero is not allowed

Therefore, I'm thinking that something is wrong with my velocity function but up till now I can't still figure it out

Thank you in advance!

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# Homework Help: Finding velocity function from a model of force

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