I just realized that I have some issues with physics: I cannot just convert Power to Force (different units), $P = F * v$.
But am I not able to calculate the force on a car that accelerates with a 100 kiloWatt engine without knowing any other parameters? If yes, how? If no, why?
Power is defined as the derivative of the work done onto something with respect to the time, namely $P=\dot{W}$. Integrating over the duration of the time interval gives you the work done by the engine on the car: $$ W=\int_0^t dt' P(t') $$ which in turn is the differential form associated to the force vector field, that is $$ dW = F_xdx + F_ydy + F_zdz $$ but also, as above $$ dW = P(t) dt. $$ Comparing the two right hand sides will give you back an equation containing the power in terms of the components of the force field. In the simple case where all the quantities are constant and do not depend on time you can easily see that this leads to something like the scalar product between $$ P(t)=\textbf{F}(t)\cdot\textbf{v}(t) $$ which I reckon is the equation you wanted to start with.
