The engine of a passenger vehicle generates a maximum power of 200 hp. At one instance, it is loaded to a total mass of 4500 kg. Engine and transmission losses dissipate 25% of the power generated by the engine, while 75% is successfully transferred to the drive wheels. Using a mass distribution where the drive wheels bear 60% of the loaded vehicle mass, determine the time the vehicle takes to attain maximum power output. Assume the vehicle accelerates at a_max on a surface with a static friction coefficient, μₛ = 1.12.