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    A crystal suspended in a chemical solution is increasing in size over time. The rate of increase of volume is inversely proportional to the square of its volume. Initially, the crystal had a volume of 3cm^3 and, one day later, its volume was 4cm^3. How long will it take for its volume to increase to 10cm^3.
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    (Original post by Improvement)
    A crystal suspended in a chemical solution is increasing in size over time. The rate of increase of volume is inversely proportional to the square of its volume. Initially, the crystal had a volume of 3cm^3 and, one day later, its volume was 4cm^3. How long will it take for its volume to increase to 10cm^3.
    solve the differential equation
    dv/dt = k/v2 subject to t=0 v=3, t=1 v=4
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    (Original post by TeeEm)
    solve the differential equation
    dv/dt = k/v2 subject to t=0 v=3, t=1 v=4
    So from this can you work out K? Or do you have to do for example, dv/dt = dv/dr x dr/dt?
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    So from this can you work out K? Or do you have to do for example, dv/dt = dv/dr x dr/dt?
    dt/dv = ??
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    (Original post by dtox)
    dt/dv = ??
    what?
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    (Original post by Improvement)
    what?
    Can you figure out what dt/dv is equal to? There's no need to mess about with variables, just look at the original equation.
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    (Original post by dtox)
    Can you figure out what dt/dv is equal to? There's no need to mess about with variables, just look at the original equation.
    dV/dt = k/v^2 ??
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    (Original post by Improvement)
    dV/dt = k/v^2 ??
    ∫v² dv = ∫k dt

    It should be easy from there.
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