Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0 V batteries of a 740 kg electric car be able to supply:

(a) To accelerate from rest to 25.0 m/s in 1.00 min?

(b) To climb a 200 m high hill in 2.00 min at a constant 25.0 m/s speed while exerting 475 N of force to overcome air resistance and friction?

(c) To travel at a constant 25.0 m/s speed, exerting a 475 N force to overcome air resistance and friction?

To find the current that the 12.0 V batteries must supply for each scenario, we need to use the power equation:

Power = Voltage × Current

Given that the efficiency of the motor is 95.0% or 0.95, the effective power produced by the motor is:

Effective Power = Efficiency × Power

For each scenario, we'll need to calculate the power required and then divide it by the battery voltage to find the current.

(a) To accelerate from rest to 25.0 m/s in 1.00 min:

First, we need to find the work done to accelerate the car using the equation:

Work = (1/2) × mass × velocity^2

Plugging in the given values, we have:

Work = (1/2) × 740 kg × (25.0 m/s)^2

Next, we need to find the time taken in seconds, given that it is given in minutes:

Time = 1.00 min × 60 s/min

Using the equation for power, we can find the power required:

Power = Work / Time

Finally, we can calculate the current:

Current = Power / Voltage

(b) To climb a 200 m high hill in 2.00 min at a constant 25.0 m/s speed while exerting 475 N of force to overcome air resistance and friction:

First, we calculate the power required using the equation:

Power = force × velocity

Power = 475 N × 25.0 m/s

Next, we convert the time to seconds:

Time = 2.00 min × 60 s/min

Now we can calculate the current:

Current = Power / Voltage

(c) To travel at a constant 25.0 m/s speed, exerting a 475 N force to overcome air resistance and friction:

Similar to the previous scenario, we calculate the power required using the equation:

Power = force × velocity

Power = 475 N × 25.0 m/s

Finally, we can calculate the current:

Current = Power / Voltage

Remember that these calculations are based on the given assumptions, and they may not account for all real-world factors.