An electric car is equipped with an electric motor supplied by a bank of sixteen 12-V batteries. When fully charged each battery supplies 2.2 MJ of total energy. With the motor delivering 9 kW of power, the car has a speed of 65 km/h (on a level road). How far can the car travel before its batteries run down? (Neglect any internal losses to friction etc.)Select one:a.65 kmb.71 kmc.110 kmd.55 kme.98 kmClear my choice
Question
An electric car is equipped with an electric motor supplied by a bank of sixteen 12-V batteries. When fully charged each battery supplies 2.2 MJ of total energy. With the motor delivering 9 kW of power, the car has a speed of 65 km/h (on a level road). How far can the car travel before its batteries run down? (Neglect any internal losses to friction etc.)Select one:a.65 kmb.71 kmc.110 kmd.55 kme.98 kmClear my choice
Solution
First, we need to find the total energy supplied by the batteries. Since each battery supplies 2.2 MJ of energy and there are 16 batteries, the total energy is:
E_total = 16 batteries * 2.2 MJ/battery = 35.2 MJ
We need to convert this energy to the same units as the power of the motor, which is given in kW. There are 1000 J in 1 kJ, and 3600 seconds in 1 hour, so:
E_total = 35.2 MJ * (1000 kJ/MJ) * (1 hour/3600 kJ) = 9.8 kWh
The time that the car can run before the batteries run down is the total energy divided by the power:
t = E_total / P = 9.8 kWh / 9 kW = 1.09 hours
The distance that the car can travel is the speed times the time:
d = v * t = 65 km/h * 1.09 hours = 70.85 km
So, the car can travel approximately 71 km before its batteries run down. The closest answer is (b) 71 km.
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