Power and energy Energy is the capacity to do work, and power is the rate at which energy...

Power and energy Energy is the capacity to do work, and power is the rate at which energy is used or consumed. Therefore, if E(t) is the energy function for a system, then P(t) = E′(t) is the power function. A unit of energy is the kilowatt-hour (1 kWh is the amount of energy needed to light ten 100-W lightbulbs for an hour); the corresponding units for power are kilowatts. The following figure shows the energy consumed by a small community over a 25-hour period.

a. Estimate the power at t − 10 and t = 20 hr. Be sure to include units in your calculation.

b. At what times on the interval [0, 25] is the power zero?

c. At what times on the interval [0, 25] is the power a maximum?