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

Question:

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 light bulbs 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?

EA 350 300 y = E(t) 250 15 5 10 25 Time (hr) Energy (kWh) 20