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A lightweight electric car is powered by ten 13V batteries. At a speed of 82km/h

ID: 1320832 • Letter: A

Question

A lightweight electric car is powered by ten 13V batteries. At a speed of 82km/h the average frictional force is 1111N. I have already solved correctly that the power of the electric motor must be 25.3061 kW to travel at a speed of 82km/h, that if each battery can delicer 154A*h of charge before recharging, a total charge of 5.544 MC are delivered by the 10 batteries before charging, that the total electrical energy delivered by the 10 batteries before recharging is 72.072MJ, and lastly, that the car can travel at 82km/h a distance of 64.87128123 km before the batteries must be recharged. My question is: what is the "driving cost" if the cost of recharging the batteries is $0.70 / kW*h? The answer must be given in dollars/km. I'm pretty bad with converting things, and I think that is what I'm struggling with in this question..

Explanation / Answer

work or energy is force x distance.
to change to power, divide that by time
82 km/hour = 22.7 m/s
so power required to drive 22.7 m/s is
P = 1111 x 22.7meter / 1 sec

=25219.7

=25.2 kW

154 amp-hr x 10 = 1540 amp-hour
or 1540 (C/s) x 3600 s = 5.54 MC

154 amp-hr x 10 = 1540 amp-hour
1540 amp-hour x 13v = 20020 watt-hour
20020 watt-hour x 3600 sec/hour = 72.07 MJ

25.3 kwatt-hour / 25.2 kW / = 1.003 hour
1.003 hour x 82 km/hr = 82.32 km

25.3 kwatt-hour x $0.70 / kWh = $17.71/hour

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