β=0.01;
γ=0.01;
vo=100;

sol=NDSolve[{v'[t]==-β v[t] - γ ((v[t])^2),v[0]==vo},v[t],{t,0,100}]
LogPlot[Evaluate[v[t]/.sol],{t,0,100}, PlotRange->{0,vo},AxesLabel->{"t (sec)","velocity (m/s)"}]