Velocity over time with constant power

[watarok]

For a car with constant power, how will its velocity change over time?

Since power (P) is the derivative of the kinetic energy (Ek), I've found that the equation for the velocity as a function of time is √(2*P*t/m). Is this correct? Would the graph then be a root graph?

 

[elegysix]

so P = F*v, which means v = P/F. and F = mdv/dt... therefore vdv=Pdt/m which leads to $v=\sqrt{(2Pt/m)}$, so yeah I think you've got it right.