1. (30 points) As an engineer at an electric car company, you are tasked to analyze...

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1. (30 points) As an engineer at an electric car company, you are tasked to analyze the acceleration characteristics of an electric car during its design stage. To simplify the analysis, it is assumed that this car can generate a constant maximum power of Pmax = 200 kW. The power is calculated by multiplying the force generated by the car and its velocity (i.e., P = fv). When the mass of the car is m = 2000 kg, find the minimum time it takes for the car to accelerate from Vmin = 0 km/hr (0 m/s) to Vmax = 100 km/hr (27.7778 m/s). The static and dynamic friction coefficients between its tires and the road surface are measured as = 0.8 and k = 0.5, respectively. The gravitational acceleration is g = 9.8 m/s. For a simplification, assume that the road surface is leveled and the car is moving along a straight line. If necessary, make any additional assumptions. (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. (30 points) As an engineer at an electric car company, you are tasked to analyze the acceleration characteristics of an electric car during its design stage. To simplify the analysis, it is assumed that this car can generate a constant maximum power of Pmax = 200 kW. The power is calculated by multiplying the force generated by the car and its velocity (i.e., P = fv). When the mass of the car is m = 2000 kg, find the minimum time it takes for the car to accelerate from Vmin = 0 km/hr (0 m/s) to Vmax = 100 km/hr (27.7778 m/s). The static and dynamic friction coefficients between its tires and the road surface are measured as = 0.8 and k = 0.5, respectively. The gravitational acceleration is g = 9.8 m/s. For a simplification, assume that the road surface is leveled and the car is moving along a straight line. If necessary, make any additional assumptions. (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.