\(\frac{dQ}{dL} = (S_{iL}-S_i)wvt = \frac{dS}{dt}\)\\
\(\int \frac{dS}{(S_{iL}-S_i)} = wv\int tdt\)\\
\(\lg(S-S_0) = wv\frac{t^2}{2} + C\)\\
\(S - S_0 = e^{wv\frac{t^2}{2}}\)\\
\(S = S_0 + e^{wv\frac{t^2}{2}}\)\\
\(S = 50 + e^{200*\frac{1}{60}*\frac{t^2}{2}}\)\\