Your Uber driver is taking you from the beach toward the esplanade tram stop because you are too exhausted to walk up the 5-degree (α=5^0) incline hill. The Uber is driving a Holden Commodore (m=1700 kg). At the base of the hill, the driver’s speed is showing v_0=20 km/h, here the driver begins to accelerate to reach the top of the gradient. The coefficient of static friction between the tyres and the asphalt is given as μ=0.13. The wind is severe on the beachfront, so you will need to consider air resistance caused by a poorly designed spoiler on the vehicle (F_air=0.8v^2). The force exerted by the motor can be considered as F_m. A. Given the acceleration of the vehicle is maximum at 1.67 m/s^2, find the analytical expression for the motor power in time. B. Assuming the maximum power output of the motor is 525 kW, how long can the vehicle maintain the acceleration (express answer in seconds, s).

Your Uber driver is taking you from the beach toward the esplanade tram stop because you are too exhausted to walk up the 5-degree (α=5^0) incline hill. The Uber is driving a Holden Commodore (m=1700 kg). At the base of the hill, the driver’s speed is showing v_0=20 km/h, here the driver begins to accelerate to reach the top of the gradient. The coefficient of static friction between the tyres and the asphalt is given as μ=0.13. The wind is severe on the beachfront, so you will need to consider air resistance caused by a poorly designed spoiler on the vehicle (F_air=0.8v^2). The force exerted by the motor can be considered as F_m. A. Given the acceleration of the vehicle is maximum at 1.67 m/s^2, find the analytical expression for the motor power in time. B. Assuming the maximum power output of the motor is 525 kW, how long can the vehicle maintain the acceleration (express answer in seconds, s).

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