a 12 V car battery is found to be capable of storing 2.0 kW*h of eletrical energy. for a certain eletric car, it is necessary to develop 10 kW of power to drive at 20 km/h.
a)suppose that the car has 10 such batteries. how long(hours)could it run if all 10 of them released all of their energy?
b)how far(kilemetres)can the car go on its 10 battries if they are fully charged?
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To answer these questions, we need to understand the relationship between power, energy, and time.
Power (P) is the rate at which energy is transferred or used. It is calculated as the energy (E) divided by the time (t):
P = E / t
In this case, the power required to drive the electric car is given as 10 kW (kilowatts) and the energy stored per battery is given as 2.0 kW*h (kilowatt-hours). We'll use this information to find the time and distance.
a) To find out how long the car could run if all 10 batteries released all of their energy, we'll first calculate the total energy stored in 10 batteries:
Total energy = 10 batteries * 2.0 kW*h/battery = 20.0 kW*h
Now, we'll use the power requirement to find the time:
Power = Energy / Time
10 kW = 20.0 kW*h / Time
10 kW * Time = 20.0 kW*h
Time = 20.0 kW*h / 10 kW = 2.0 hours
Therefore, if all 10 batteries released all of their energy, the car could run for 2.0 hours.
b) To find out how far the car can go on its 10 batteries if they are fully charged, we'll use the power requirement and the energy stored per battery. First, we need to convert the power requirement from kilowatts to watts:
10 kW = 10,000 watts
Now, we'll convert the energy stored per battery from kilowatt-hours to watt-hours:
2.0 kW*h = 2,000 watt-hours
Next, we use the formula:
Power = Energy / Time
Rearranging the formula to solve for time:
Time = Energy / Power
Time = 2,000 watt-hours / 10,000 watts = 0.2 hours
Now, we can find the distance (D) using the formula:
Distance = Speed * Time
The speed is given as 20 km/h (kilometers per hour), and the time is converted to hours:
Distance = 20 km/h * 0.2 hours = 4 km
Therefore, the car can go a distance of 4 kilometers on its 10 fully charged batteries.