A lightweight electric car is powered by a series combination of ten 12. 0-V bat

Question

A lightweight electric car is powered by a series combination of ten 12. 0-V batteries, each having negligible internal resistance. Each battery can deliver a charge of 142 A h before needing to be recharged. At a speed of 100 km/h, the average frictional force due to air drag and rolling friction is 1. 4 kN. What must be the minimum power delivered by the electric motor if the car is to travel at a speed of 100 km/h? What is the total charge, in coulombs, that can be delivered by the series combination of ten batteries before recharging is required? What is the total electrical energy delivered by the 10 batteries before recharging? How far can the car travel (at 100 km/h) before the batteries must be recharged? What is the cost per kilometer if the cost of recharging the batteries is 9 cents per kilowatt-hour?

Explanation / Answer

1) P=Fv = 1.4*10^3 * 100*5/18 = 38.889 kW
2) 1 ampere hour = 3600 C
10*142 Ah= 10*142*3600=5112kC
3) E=qv= 61344kJ

4)P =VI
38.889*10^3=(12*10)*I
I = 324A

q=It
142*10/324=t
t= 4.38 hours

distance= 100*4.38= 438km

5) 1kWh = 3600kJ

61344/3600 = 17.04kWh
coust = 17.04*.09 = $1.5336
1.5336/438 = 3.0513699e-3

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