Final answer:
To find the current required by the batteries to accelerate the electric car, we can use the principle of conservation of energy. The electrical power supplied by the batteries will be converted into kinetic energy to accelerate the car. By calculating the expression, we find that the current required by the batteries to accelerate the electric car is approximately 545 A.
Step-by-step explanation:
To find the current required by the batteries to accelerate the electric car, we can use the principle of conservation of energy. The electrical power supplied by the batteries will be converted into kinetic energy to accelerate the car.
First, let's calculate the change in kinetic energy of the car:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
ΔKE = KE_final - KE_initial
Next, we need to find the work done by the motor to accelerate the car:
Work (W) = ΔKE
Since the motor has an efficiency of 95%, we can calculate the electrical power needed:
Electrical Power = W / efficiency
Finally, using Ohm's Law (V = I * R), we can find the current:
Current (I) = Electrical Power / Voltage
Plugging in the values, we have:
ΔKE = 0.5 * 708 kg * (14 m/s)^2 - 0.5 * 708 kg * (0 m/s)^2
W = ΔKE = 0.5 * 708 kg * (14 m/s)^2
Electrical Power = W / efficiency = 0.5 * 708 kg * (14 m/s)^2 / 0.95
Current = Electrical Power / Voltage = (0.5 * 708 kg * (14 m/s)^2 / 0.95) / 12 V
By calculating the expression, we find that the current required by the batteries to accelerate the electric car is approximately 545 A .