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# Power and energy Energy is the capacity to do work and ## Problem 57E Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Problem 57E

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 light bulbs for an hour); the corresponding units for power are kW. The following figure shows the energy consumed by a small community over a 25-hr period. a.? Estimate the power at ?t? = 10 and ?t? = 20 hr. Be sure to include units in your calculation. b.? At what limes on the interval [0, 25] is the power zero? c.? At what times on the interval [0, 25] is the power a maximum?

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SOLUTION STEP 1 Given energy = E(t). d Then power P(t) = dtE(t) = E(t) Given, 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 kW. The following figure shows the energy consumed by a small community over a 25-hr period. STEP 2 An estimated graph of its derivative can be drawn as follows(ie,...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

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Power and energy Energy is the capacity to do work and

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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 57e

Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 57e