An electric car is designed to run on a bank of batteries...

An electric car is designed to run on a bank of batteries with a total potential difference of $12 \mathrm{V}$ and a total energy storage of $2.0 \times 10^{7}$ ). a. If the electric motor draws $8.0 \mathrm{kW}$, what is the current delivered to the motor? b. If the electric motor draws $8.0 \mathrm{kW}$ as the car moves at a steady speed of $20.0 \mathrm{m} / \mathrm{s}$, how far will the car travel before it is "out of juice"?

An electric car is designed to run on a bank of batteries with a total potential difference of $12 \mathrm{V}$ and a total energy storage of $2.0 \times 10^{7}$ ).
a. If the electric motor draws $8.0 \mathrm{kW}$, what is the current delivered to the motor?
b. If the electric motor draws $8.0 \mathrm{kW}$ as the car moves at a steady speed of $20.0 \mathrm{m} / \mathrm{s}$, how far will the car travel before it is "out of juice"?

Key Concepts

Energy Storage

Energy storage in a battery is the total amount of energy that can be supplied over time, typically measured in joules (J) or watt-hours (Wh). This concept is essential for determining how long an energy source can sustain a given power demand before it is depleted.

Electric Current

Electric current is the flow rate of electric charge through a conductor, measured in amperes (A). The relationship between current, voltage, and power in a circuit is given by the equation P = IV, which enables the calculation of one quantity if the other two are known.

Relationship Between Energy, Power, and Time

The relationship between energy, power, and time is expressed by the equation Energy = Power × Time. This equation allows one to calculate the duration for which a device can operate given its power consumption and the stored energy available, thereby linking electrical performance with operational time.

Electric Power

Electric power is the rate at which energy is transferred or converted per unit time. It is measured in watts (W) where one watt equals one joule per second. In many electrical problems, power is related to other quantities like voltage and current, which helps determine the behavior of electrical circuits and devices.

Voltage

Voltage, often referred to as the electric potential difference, is a measure of the energy per unit charge available to drive electrons through a circuit. It is measured in volts (V) and plays a crucial role in determining how much current will flow for a given amount of power consumption.

Kinematics (Distance = Speed × Time)

Kinematics is the branch of mechanics that deals with the motion of objects. In scenarios where an object moves with a constant speed, the distance traveled can be calculated using the relation Distance = Speed × Time. This concept connects the time over which energy is used to motion outcomes, such as the distance covered by a vehicle.

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