A car generates a constant maximum power of Pmax=200kW. The power is calculated by multiplying the force generated by the car and its velocity (i.e., Power=Force*velocity). The mass of the car is m=2000kg. vmin= 0 km/h(0m/s)to vmax=100km/h(27.7778m/s). The static and kinetic friction coefficients between its tires and the road surface are measured as us=0.8 and uk=0.5, respectively. g=9.81m/s^2. Assume that the road surface is horizontal, the car is moving along a straight line, and the rotary inertial of tires is ignored.

(Hint) Since the power is constant, the force (F=P/v) generated by the car can be extremely high in a low-speed region. Thus, the force should be limited not to slip for the maximum performance in the low-speed region (which is referred to as a low-speed traction control). Then, this problem should be analyzed in two speed regions: the low-speed region with the torque limit and the high-speed region without the torque limit.

1) Find the velocity between the low- and high-speed regions. [vcritical m/s] Round your answer to the nearest hundredth.

 

2) Find the time from 0 to vc in seconds. Round your answer to the nearest hundredth.

 

3) Find the minimum time from 0 to vmax = 100km/s in seconds. Round your answer to the nearest hundredth.