A) A lightweight electric car is powered by ten 12-V batteries. At a speed of 70

Question

A)
A lightweight electric car is powered by ten 12-V batteries. At a speed of 70 km/h, the average frictional force is 1050 N. What must be the power of the electric motor if the car is to travel at a speed of 70 km/h?

B)
If each battery can deliver a total charge of 180 Ah before recharging, what is the total charge in coulombs that can be delivered by the ten batteries before recharging?

C)
What is the total electric energy delivered by the ten batteries before recharging?

D)
How far can the car travel at 70 km/h before the batteries must be recharged?

E)
What is the cost per kilometer if the cost of recharging the batteries is 9 cents per kilowatt-hour? (Give your answer in cents. Don't give units)

Explanation / Answer

A.)power = Fv = 1050*70*5/18 = 20416.67 W

B). charge from each battery = 180*3600 C
Total charge = 10*180*3600C = 6.48 * 106C

C).total electric energy = qV = 6.48*12 * 106J

D).energy delivered per second by the motor = 20416.67J

So time needed for 6.48*12 * 106J to be delivered = 6.48*12 * 106J/20416.67J = 3808.65s = 1.058hrs

So, distance travelled in that time = 70*5/18 * 3808.65 = 74.057km

E).1kWh = 1000*3600 J

time taken for 1km = 1/70hr = 51.43s

So energy spent in 51.43 secs = 20416.67 * 51.43

1000*3600 J costs 9 cents

So,20416.67 * 51.43 J will cost 2.625cents

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