newtonian mechanics - Numerical method for first-order non-linear differential equation

So I'm modeling a cycler on a 1000 m race track using the equation $$\frac{dv}{dt}=\frac{P}{m}\left(\frac{1}{v}\right)-\frac{k}{m}\left(v^2\right)-ug$$ where $P$ = power, $m$ = mass, $v$ = velocity of cycler, $k$ = drag coefficient, $u$ = kinetic friction and $g$ = gravity.

Now logical, the cycler will start at $v = 0$ for $t = 0$, i.e. $v(0)=0$ (initial condition) but when I use Euler's Method, it says that the initial condition is not part of the domain.

Now my questions

1. Then what should I use as the initial condition


2. How can I calculate the next $v$, i.e $v(t+h$) where $h$ is the step size


3. How can I simulate the race and plot the velocity-time graph?



4. How can I plot the distance-time graph?

What would be a more accurate model? Thank you