A modern electric car carries a battery with a 300~\text{MJ} ( 3 \times 10^{8}~\text{Joule} )300 MJ(3×10 8 Joule) energy capacity. If the power used by the car while traveling at a steady pace of 25 \frac{m}{s}25 s m is measured to be 17.7~\text{kW}17.7 kW, estimate the maximum driving range of the car on a full battery. Give your answer in kilometers

Given Information:

Battery capacity = 300 MJ

Speed = 25 m/s

Pcar = 17.7 kW

Required Information:

Range = D = ?

Range = D =  423.7 km

Explanation:

Convert battery capacity from joules to kWh

Battery capacity = 300x10⁶/3600

Battery capacity = 83333.33 Wh = 83.33 kWh

Convert speed of the car from m/s to km/h

speed = 25 m/s = 25*3.6 = 90 km/h

Pcar = 17.7 kW

Find the kW used per km

kW per km = Pcar/speed = 17.7/90 = 0.19666 kWh/km

Find the range of the car

Range = D = Battery capacity/kW per km

Range = D = 83.33/0.19666 = 423.7 km