Class 9 Science NCERT Notes – Chapter 10: Work and Energy (PDF, MindMap, Q&A, Quizzes)

Chapter 10 (Physics): Work and Energy – Class 9 NCERT Science Detailed Study Notes.

1. The Concept of Work

1.1 Everyday vs. Scientific Definition of Work

In daily life, “work” refers to any useful physical or mental labor. Activities like studying for an exam, reading books, or thinking are considered “hard work.” However, in science, the definition is much more specific and may not align with our common understanding.

For example, pushing against a huge rock that does not move is exhausting, but scientifically, no work is done on the rock. Similarly, holding a heavy load on your head without moving involves effort and energy expenditure, but no work is done on the load. In contrast, climbing a staircase involves a significant amount of scientific work.

1.2 The Scientific Conception of Work

For work to be done from a scientific perspective, two fundamental conditions must be satisfied:

1. A force must act on an object.
2. The object must be displaced (i.e., it must move).

If either of these conditions is not met, no work is done. For instance, if the force on an object is zero or the displacement is zero, the work done is zero.

1.3 Work Done by a Constant Force

When a constant force acts on an object, and the object is displaced in the direction of the force, the work done is defined as the product of the force and the displacement.

• Formula: Work done (W) = Force (F) × displacement (s)
• Equation: W = Fs

Work is a scalar quantity, meaning it has only magnitude and no direction.

1.4 Unit of Work: The Joule

The standard unit of work is the newton-meter (N m), which is also called the joule (J), in honor of James Prescott Joule.

• Definition of 1 Joule: One joule is the amount of work done on an object when a force of 1 Newton displaces it by 1 meter along the line of action of the force.

1.5 Positive and Negative Work

The work done by a force can be positive or negative, depending on the direction of the force relative to the displacement.

• Positive Work: Work is considered positive when the force applied is in the same direction as the object’s displacement. For example, when a baby pulls a toy car forward, the work done by the baby is positive.
• Negative Work: Work is considered negative when the force acts in the direction opposite to the displacement. For example, a retarding force (like friction) applied to a moving object does negative work. The work done by the force of gravity on an object lifted upwards is also negative.

2. Energy

2.1 Definition and Unit of Energy

Energy is defined as the capability to do work. An object that possesses energy can exert a force on another object and cause displacement.

• Energy Transfer: When an object does work, it loses energy. The object on which the work is done gains energy.
• Unit of Energy: The unit of energy is the same as the unit of work: the joule (J). A larger unit, the kilojoule (kJ), is also used, where 1 kJ = 1000 J.

2.2 Forms of Energy

Energy exists in many forms in the world. Key forms include:

• Mechanical Energy: The sum of potential and kinetic energy.
• Heat Energy
• Chemical Energy
• Electrical Energy
• Light Energy

The Sun is the biggest natural source of energy for us, and many other energy sources are derived from it. Other sources include the nuclei of atoms, the interior of the Earth, and tides.

2.3 Kinetic Energy (Ek)

Kinetic energy is the energy possessed by an object due to its motion. Any moving object, from a speeding car to flowing water, possesses kinetic energy. The kinetic energy of an object increases with its speed.

• Definition: The kinetic energy of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity from a stationary position.
• Formula: For an object of mass m moving with a uniform velocity v: Ek = ½ mv²

The work done on an object is equal to the change in its kinetic energy. W = Change in kinetic energy = E_kf - E_ki

2.4 Potential Energy (Ep)

Potential energy is the energy present in an object by virtue of its position or configuration. It is essentially stored energy.

• Examples:
  • A stretched or compressed spring.
  • A stretched rubber band.
  • Water stored at a height in a dam.
  • The wound spring of a toy car.
  • A stretched bow.
• Gravitational Potential Energy: This is the energy an object possesses because of its height above a reference level (like the ground). Work is done against gravity to lift the object, and this work is stored as gravitational potential energy.
  • Formula: For an object of mass m raised to a height h against gravity g: Ep = mgh
  • Note: The work done by gravity depends only on the difference in the vertical heights of the initial and final positions, not on the path taken.

3. Law of Conservation of Energy

This is a fundamental principle of physics.

• Statement: Energy can only be converted from one form to another; it can neither be created nor destroyed. The total energy before and after any transformation remains the same (constant).
• Interconvertibility: Various forms of energy can be converted into one another. For example, green plants convert light energy into chemical energy (food), and a battery converts chemical energy into electrical energy.
• Mechanical Energy Conservation: In the absence of forces like air resistance, the total mechanical energy (sum of kinetic and potential energy) of a system remains constant.
  • Formula: Potential Energy + Kinetic Energy = Constant
  • mgh + ½ mv² = Constant
  • Example (Free Fall): As an object falls freely, its potential energy decreases, while its kinetic energy increases. The decrease in potential energy at any point is exactly equal to the increase in kinetic energy.

4. Power

4.1 Definition of Power

Power measures the speed of work done or the rate at which energy is transferred or consumed. A more powerful agent can do the same amount of work in less time.

• Formula: Power (P) = Work (W) / time (t)
• Equation: P = W / t

4.2 Unit of Power: The Watt

The SI unit of power is the watt (W), named in honor of James Watt.

• Definition of 1 Watt: One watt is the power of an agent that does work at the rate of 1 joule per second (1 W = 1 J/s).
• Larger Unit: The kilowatt (kW) is often used. 1 kW = 1000 W = 1000 J/s.

4.3 Average Power

Since the rate of doing work may not be constant, the concept of average power is useful.

• Definition: Average power is calculated by dividing the total energy consumed by the total time taken.

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Q&A Section

Short-Answer Questions

(Answer in 2-3 sentences.)

1. Explain the two essential conditions for scientific work to be done.
2. Why is no scientific work done when a person pushes against an unmovable wall, even though they get tired?
3. Define one joule of work.
4. What is the difference between positive and negative work? Provide an example for each.
5. What is energy, and what is its standard unit?
6. List five different forms of energy mentioned in the text.
7. What is kinetic energy? On what two factors does it depend?
8. State the formula for kinetic energy and define each variable.
9. What is potential energy? Give an example related to an object’s configuration.
10. Explain what gravitational potential energy is.
11. State the formula for gravitational potential energy and define each variable.
12. Why is the work done by gravity independent of the path taken when an object is raised from one point to another?
13. State the law of conservation of energy.
14. What is meant by the total mechanical energy of an object?
15. Describe the energy transformation that occurs as an object falls freely from a height.
16. How is the work done on an object related to its kinetic energy?
17. What is power, and how is it calculated?
18. Define one watt of power.
19. If two people do the same amount of work, but one does it faster, who has expended more power? Explain why.
20. In the process of a battery lighting a bulb, describe the energy changes that occur.
21. What happens to the kinetic energy of a freely falling object when it eventually stops upon reaching the ground?
22. Explain how a stretched bow is an example of potential energy being used to create kinetic energy.
23. The Sun is described as the biggest natural source of energy. Name two other sources of energy mentioned in the text.
24. How is the work done by a retarding force, like friction, characterized?
25. Define average power and explain when this concept is useful.

Multiple Choice Questions

1. According to the scientific definition, which of the following scenarios involves work being done?
   • a) A student studying for an exam for three hours. b) A man holding a 50 kg box on his head while standing still. c) A windmill lifting water from a well. d) A person pushing hard against a stationary truck.
2. What is the unit of work in the SI system?
   • a) Newton b) Watt c) Pascal d) Joule
3. If a force of 10 N is applied to an object and it moves 5 m in the direction of the force, how much work is done?
   • a) 2 J b) 15 J c) 50 J d) 0.5 J
4. Work done is considered negative when the force acts:
   • a) Perpendicular to the direction of displacement. b) In the same direction as the displacement. c) Opposite to the direction of displacement. d) When there is no displacement.
5. An object having the capability to do work is said to possess:
   • a) Power b) Energy c) Force d) Momentum
6. The energy possessed by an object due to its motion is called:
   • a) Potential energy b) Mechanical energy c) Kinetic energy d) Chemical energy
7. The formula for kinetic energy is: a) mgh b) Fs c) ½ mv² d) W/t
8. If the velocity of an object is doubled, its kinetic energy becomes:
   • a) Half b) Double c) Four times d) Unchanged
9. The energy stored in a stretched rubber band is an example of:
   • a) Kinetic energy b) Potential energy c) Heat energy d) Light energy
10. The gravitational potential energy of an object depends on its mass, height, and:
    • a) Its velocity b) The acceleration due to gravity c) The path taken to reach the height d) Its volume
11. According to the law of conservation of energy, energy can be:
    • a) Created but not destroyed. b) Destroyed but not created. c) Created and destroyed. d) Transformed from one form to another.
12. For a freely falling object, the sum of its potential and kinetic energy at any point is:
    • a) Increasing b) Decreasing c) Constant d) Zero
13. The rate of doing work is defined as:
    • a) Energy b) Power c) Force d) Displacement
14. The SI unit of power is the:
    • a) Joule (J) b) Newton (N) c) Watt (W) d) Kilowatt-hour (kWh)
15. One kilowatt (kW) is equal to: a) 100 W b) 1000 W c) 1 J/s d) 100 J/s
16. A porter lifts luggage of 15 kg to a height of 1.5 m. How much work does he do on the luggage? (Use g = 10 m/s²)
    • a) 15 J b) 22.5 J c) 150 J d) 225 J
17. The work done on an object is zero if the:
    • a) Force is very large. b) Velocity is constant. c) Displacement is zero. d) Mass is very small.
18. What is the total mechanical energy of an object?
    • a) The product of its kinetic and potential energy. b) The sum of its kinetic and potential energy. c) Only its kinetic energy. d) Only its potential energy.
19. A lamp consumes 1000 J of electrical energy in 10 seconds. What is its power?
    • a) 10 W b) 100 W c) 1000 W d) 10000 W
20. A girl weighing 400 N climbs a rope 8 m high in 20 seconds. What is her power output?
    • a) 64 W b) 160 W c) 3200 W d) 8000 W

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Answer Keys

Short-Answer Question Answers

1. For work to be done scientifically, a force must act on an object, and the object must be displaced. If either of these conditions is not met, no work is performed.
2. Although the person expends energy, no scientific work is done on the wall because there is no displacement. For work to be done, the force must cause the object to move.
3. One joule is the amount of work done when a force of 1 Newton displaces an object by 1 meter in the direction of the force.
4. Positive work is done when the force is in the direction of displacement, like pushing a cart forward. Negative work is done when the force opposes the displacement, such as the force of gravity on an object being lifted upwards.
5. Energy is the capability of an object to do work. Its standard unit is the joule (J), which is the same as the unit for work.
6. The five forms of energy listed are mechanical energy (potential + kinetic), heat energy, chemical energy, electrical energy, and light energy.
7. Kinetic energy is the energy an object possesses due to its motion. It depends on the object’s mass (m) and its velocity (v).
8. The formula is Ek = ½ mv², where Ek is the kinetic energy, m is the mass of the object, and v is its velocity.
9. Potential energy is the energy stored in an object due to its position or configuration. An example is the energy stored in the stretched string of a bow.
10. Gravitational potential energy is the energy an object possesses due to its height above a reference point, like the ground. It is equal to the work done against gravity to lift the object to that height.
11. The formula is Ep = mgh, where Ep is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.
12. Work done by gravity depends only on the difference in the vertical heights of the initial and final positions. This is because the gravitational force is vertical, so only the vertical component of displacement contributes to the work done by it.
13. The law of conservation of energy states that energy can only be converted from one form to another; it can neither be created nor destroyed. The total energy in a system remains constant.
14. The total mechanical energy of an object is the sum of its kinetic energy and potential energy.
15. As an object falls freely, its potential energy is converted into kinetic energy. The potential energy decreases as height decreases, while kinetic energy increases as its velocity increases.
16. The work done on an object is equal to the change in its kinetic energy. This means that work done can increase or decrease the object’s kinetic energy.
17. Power is the rate of doing work or the rate of energy transfer. It is calculated by dividing the work done (W) by the time taken (t).
18. One watt is the power of an agent which does work at the rate of 1 joule per second (1 J/s).
19. The person who does the work faster has expended more power. Power is work divided by time, so for the same amount of work, a smaller time results in greater power.
20. In a battery lighting a bulb, the battery’s chemical energy is first converted into electrical energy. This electrical energy then travels to the bulb, where it is transformed into light energy and heat energy.
21. When a freely falling object stops upon hitting the ground, its kinetic energy is transformed into other forms, primarily heat energy and sound energy, due to the impact.
22. When the string of a bow is stretched, work is done, and this energy is stored as potential energy in the bow’s new shape. Upon release, this stored potential energy is converted into the kinetic energy of the arrow, causing it to fly off.
23. Besides the Sun, the text mentions energy sources such as the nuclei of atoms, the interior of the earth, and the tides.
24. A retarding force acts opposite to the direction of motion. Therefore, the work done by such a force is always negative.
25. Average power is the total energy consumed divided by the total time taken. This concept is useful when the rate of doing work varies over time, providing an overall measure of power for the entire duration.

Multiple Choice Question Answers

1. c) A windmill lifting water from a well. (Force is applied, and water is displaced).
2. d) Joule
3. c) 50 J (W = 10 N * 5 m = 50 J)
4. c) Opposite to the direction of displacement.
5. b) Energy
6. c) Kinetic energy
7. c) ½ mv²
8. c) Four times (KE is proportional to v²)
9. b) Potential energy
10. b) The acceleration due to gravity
11. d) Transformed from one form to another.
12. c) Constant
13. b) Power
14. c) Watt (W)
15. b) 1000 W
16. d) 225 J (W = mgh = 15 kg * 10 m/s² * 1.5 m = 225 J)
17. c) Displacement is zero.
18. b) The sum of its kinetic and potential energy.
19. b) 100 W (P = 1000 J / 10 s = 100 W)
20. b) 160 W (P = W/t = (400 N * 8 m) / 20 s = 3200 / 20 = 160 W)

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Essay Questions and Answers

1. Contrast the everyday meaning of “work” with its scientific definition. Provide two examples of activities that are considered “work” in daily life but involve zero scientific work, and explain why.

• Answer: In everyday language, “work” refers to any mental or physical effort, like studying, thinking, or holding a heavy object. The scientific definition of work is more precise: it is the product of a force and the displacement of an object in the direction of that force (W = Fs). This requires both a force and movement.
  • Example 1: Pushing a stationary wall. A person pushing a wall is exerting a force and using energy, which is considered hard work in daily life. However, since the wall does not move, its displacement is zero. According to the scientific formula, W = F × 0 = 0, so no work is done on the wall.
  • Example 2: Holding a heavy suitcase. A person holding a heavy suitcase stationary is using muscular effort to counteract gravity. In common terms, this is work. Scientifically, however, the suitcase is not being displaced. Since displacement is zero, no work is done on the suitcase.

2. Explain the concepts of positive work and negative work. Describe a single physical process where both positive and negative work are done simultaneously by different forces.

• Answer: Positive work is done when the applied force has a component in the same direction as the displacement. This generally means the force is helping the motion. Negative work is done when the force has a component opposite to the direction of displacement, meaning the force opposes the motion.
  • A clear example is lifting an object, like a book, from the floor to a shelf at a constant velocity. The person lifting the book exerts an upward force, and the book is displaced upwards. Therefore, the work done by the person is positive. At the same time, the force of gravity is acting downwards on the book, opposite to the upward displacement. Thus, the work done by the force of gravity is negative. In this single process, positive work is done by the lifter, and negative work is done by gravity.

3. Derive the expression for the kinetic energy of an object of mass m moving with velocity v.

• Answer: The kinetic energy of an object is defined as the work done to accelerate it from rest to a velocity v. Let an object of mass m start from rest (u = 0) and reach a velocity v after being displaced by a distance s under a constant force F.
  1. The work done on the object is W = F × s.
  2. According to Newton’s second law, F = ma, where a is the acceleration.
  3. Substituting this into the work equation gives W = (ma) × s.
  4. From the equations of motion, we know that v² - u² = 2as. Since u=0, this simplifies to v² = 2as.
  5. We can rearrange this equation to solve for s: s = v² / (2a).
  6. Now, substitute this expression for s back into the work equation: W = ma × (v² / (2a)).
  7. The acceleration a cancels out, leaving W = m × (v² / 2), which simplifies to W = ½ mv². Since the kinetic energy (Ek) is equal to the work done to bring the object to that velocity from rest, the expression for kinetic energy is Ek = ½ mv².

4. Using the example of a simple pendulum, illustrate the law of conservation of mechanical energy. Explain why the pendulum eventually comes to rest.

• Answer: The law of conservation of energy states that energy transforms but is not lost. For a simple pendulum, the total mechanical energy (sum of potential and kinetic energy) remains nearly constant.
  • At the extreme positions: When the pendulum bob is at its highest point on either side of its swing, it momentarily stops. Here, its velocity is zero, so its kinetic energy is zero. All its mechanical energy is in the form of gravitational potential energy (Ep = mgh), which is at its maximum.
  • At the mean (lowest) position: As the bob swings downwards, its height decreases, and its potential energy is converted into kinetic energy. At the lowest point of the swing (the mean position), its height is minimum (considered zero level), so its potential energy is minimum (zero). Its speed is maximum, so its kinetic energy (Ek = ½ mv²) is at its maximum.
  • During the swing: At any point between the extreme and mean positions, the bob has both potential and kinetic energy. The sum, Ep + Ek, remains constant throughout the oscillation.
  • Why it stops: The pendulum eventually comes to rest because of air resistance and friction at the pivot point. These are dissipative forces that do negative work on the pendulum, converting its mechanical energy into heat energy, which dissipates into the surroundings. This is not a violation of the law of conservation of energy, as the mechanical energy is not destroyed but transformed into another form (heat).

5. An object of mass 20 kg is dropped from a height of 4 m. Calculate its potential and kinetic energy at the start, at a height of 2 m, and just before it hits the ground. Show that total mechanical energy is conserved. (Use g = 10 m/s²).

• Answer:
  • 1. At the start (height h = 4 m):
    • The object is at rest, so velocity v = 0.
    • Potential Energy (Ep) = mgh = 20 kg × 10 m/s² × 4 m = 800 J.
    • Kinetic Energy (Ek) = ½ mv² = ½ × 20 × 0² = 0 J.
    • Total Mechanical Energy = Ep + Ek = 800 J + 0 J = 800 J.
  • 2. At mid-point (height h = 2 m):
    • The object has fallen a distance of 4 m - 2 m = 2 m.
    • Using v² = u² + 2as, v² = 0² + 2(10)(2) = 40 m²/s².
    • Potential Energy (Ep) = mgh = 20 kg × 10 m/s² × 2 m = 400 J.
    • Kinetic Energy (Ek) = ½ mv² = ½ × 20 × 40 = 400 J.
    • Total Mechanical Energy = Ep + Ek = 400 J + 400 J = 800 J.
  • 3. Just before hitting the ground (height h ≈ 0 m):
    • The object has fallen the full distance of 4 m.
    • Using v² = u² + 2as, v² = 0² + 2(10)(4) = 80 m²/s².
    • Potential Energy (Ep) = mgh = 20 × 10 × 0 = 0 J.
    • Kinetic Energy (Ek) = ½ mv² = ½ × 20 × 80 = 800 J.
    • Total Mechanical Energy = Ep + Ek = 0 J + 800 J = 800 J.
  • Conclusion: At all three points, the total mechanical energy is 800 J, demonstrating the principle of conservation of mechanical energy.

6. Define Power and its unit. Explain with an example how two individuals can do the same amount of work but expend different amounts of power.

• Answer: Power is defined as the rate at which work is done or the rate at which energy is transferred. Its formula is P = W/t. The SI unit of power is the watt (W), where 1 watt equals 1 joule per second.
  • Example: Consider two girls, A and B, each with a weight of 400 N, climbing a rope to a height of 8 m.
  • The work done by each girl is the same, calculated as Work = Force × distance = 400 N × 8 m = 3200 J.
  • Now, let’s say Girl A takes 20 seconds to climb the rope, while Girl B takes 50 seconds.
  • Power of Girl A = 3200 J / 20 s = 160 W.
  • Power of Girl B = 3200 J / 50 s = 64 W.
  • This example clearly shows that even though both girls performed the exact same amount of work (3200 J), Girl A was more powerful because she did the work in a shorter amount of time.

7. Describe the various energy transformations that occur when a person is riding a bicycle.

• Answer: Riding a bicycle involves a series of energy transformations:
  1. The rider’s body uses chemical energy stored from food to contract muscles.
  2. This chemical energy is converted into the mechanical energy of the rider’s legs pushing the pedals.
  3. The mechanical energy is transferred through the chain to the wheels, causing them to rotate. This rotational energy is a form of kinetic energy, which propels the bicycle forward.
  4. As the bicycle moves, it has kinetic energy due to its motion. If the rider goes up a hill, some of this kinetic energy is converted into gravitational potential energy.
  5. Throughout the process, some mechanical energy is lost due to friction (in the bearings, chain, and between the tires and the road) and air resistance. This lost energy is converted into heat energy. The rider also generates heat as a byproduct of metabolism.

8. Is it possible for an object to have displacement in the absence of any force acting on it? Discuss this in the context of work done.

• Answer: Yes, an object can have displacement in the absence of a net force acting on it. According to Newton’s First Law of Motion, an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Therefore, an object moving with a uniform velocity in a straight line has displacement, but the net force acting on it is zero.
  • In the context of work done, if the net force is zero (F = 0), then the work done is also zero (W = Fs = 0 × s = 0), even if there is displacement. This happens when an object is moving at a constant velocity on a frictionless surface. While the object is moving and covering a distance, no work is being done on it to maintain that motion.

9. A force acting on a 20 kg mass changes its velocity from 5 m/s to 2 m/s. Calculate the work done by the force.

• Answer: The work done by the force is equal to the change in the kinetic energy of the object.
  • Mass of the object, m = 20 kg.
  • Initial velocity, u = 5 m/s.
  • Final velocity, v = 2 m/s.
  • Initial Kinetic Energy (E_ki) = ½ mu² = ½ × 20 kg × (5 m/s)² = 10 × 25 = 250 J.
  • Final Kinetic Energy (E_kf) = ½ mv² = ½ × 20 kg × (2 m/s)² = 10 × 4 = 40 J.
  • Work Done (W) = Change in Kinetic Energy = E_kf - E_ki.
  • W = 40 J – 250 J = -210 J.
  • The negative sign indicates that the work was done by a force opposing the motion (a retarding force), which caused the object to slow down.

10. What is gravitational potential energy? Explain why its value for an object at a given position can be different depending on the reference level chosen.

• Answer: Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, specifically its height above a certain reference point. It is equivalent to the work done in lifting the object from that reference point to its current position against the force of gravity (Ep = mgh).
  • The value of potential energy is relative because it depends on the “zero level” or reference point from which the height h is measured. For example, consider a book on a table that is 1 meter high, in a room on the second floor of a building, 5 meters above the ground.
  • If we choose the tabletop as the zero level, the book’s potential energy is 0 J.
  • If we choose the floor of the room as the zero level, the book is at a height of 1 m, and its potential energy is mg(1).
  • If we choose the ground outside as the zero level, the book is at a height of 5 m, and its potential energy is mg(5).
  • All these values are correct for their respective reference frames. In physics problems, what usually matters is the change in potential energy, which is independent of the chosen zero level.

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Glossary of Key Terms

Term	Definition
Work	The product of the magnitude of the force and the distance moved by the object in the direction of the applied force (W = Fs).
Joule (J)	The SI unit of work and energy. 1 J is the work done when a force of 1 N displaces an object by 1 m.
Energy	The capability of doing work.
Kinetic Energy (Ek)	The energy possessed by an object due to its motion. It is calculated as Ek = ½ mv².
Potential Energy (Ep)	The energy possessed by a body due to its change in position or shape (configuration).
Gravitational Potential Energy	The energy of an object at a height, defined as the work done in raising it from the ground to that point against gravity (Ep = mgh).
Law of Conservation of Energy	A law stating that energy can only be transformed from one form to another; it can neither be created nor destroyed. The total energy of a system remains constant.
Mechanical Energy	The sum of the kinetic and potential energies of an object.
Power	The rate of doing work or the rate of transfer of energy. It is calculated as P = W/t.
Watt (W)	The SI unit of power. 1 W is equivalent to 1 joule per second (1 J/s).
Kilowatt (kW)	A unit of power equal to 1000 watts.
Average Power	The total energy consumed divided by the total time taken.