PhysicsICSE Class 10 · Work, Energy and Power

Power and Its Units: P = W/t, Watt and Horsepower, Solved Numericals (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Power is the rate of doing work: P = W/t. Its SI unit is the watt (1 W = 1 J s⁻¹); its cgs unit is erg s⁻¹. Larger units are the kilowatt (10³ W), megawatt (10⁶ W) and gigawatt (10⁹ W), and 1 horsepower = 746 W. At steady speed v against a force F, P = Fv.

Same work in half the time means double the power; kW is a unit of power but kW h is a unit of energy.

Illustration drawn for QuestionBuddy.

Understand Power and Its Units

Two people may do the same work, but the one who does it faster is more powerful. Power is the rate of doing work, or the rate at which energy is transferred:

$P = \frac{W}{t} .$

Power is a scalar. It depends on both the work done and the time taken: the same work in half the time means double the power.

Units.

SI unit: the watt (W). $1 W = 1 J s^{- 1}$ : a body has a power of 1 W if it does 1 J of work in 1 s.
cgs unit: erg s⁻¹. $1 W = 1 0^{7}$ erg s⁻¹.
Bigger units: kilowatt, $1 kW = 1 0^{3}$ W; megawatt, $1 MW = 1 0^{6}$ W; gigawatt, $1 GW = 1 0^{9}$ W. Power stations are rated in MW or GW.
Horsepower: $1 hp = 746$ W, used for motors, pumps and engines.

Do not confuse power and energy units. kW is a unit of power; kW h (kilowatt hour) is a unit of energy (power × time): $1 kW h = 1000 W \times 3600 s = 3.6 \times 1 0^{6}$ J.

Power when lifting. Lifting a mass $m$ through a height $h$ in time $t$ : $P = \frac{m g h}{t}$ .

Power at steady speed. If a force $F$ keeps a body moving at a steady speed $v$ in its own direction, the work in time $t$ is $F \times v t$ , so

$P = \frac{F v t}{t} = F v .$

This is useful for cars and cyclists moving at steady speed against resistance: the engine's force equals the resistance.

Comparing powers. The 2024 paper asked for the ratio of the powers of two people who did different work in different times. Method: find each power (convert all times to seconds, or at least to the same unit), then write the ratio in the order asked and simplify to whole numbers, e.g. $4 : 1$ , not $\frac{1}{1} : \frac{1}{4}$ or $1 : 4$ .

Average power. If the rate of working varies, $\frac{W}{t}$ gives the average power over that time.

Power and energy together. Rearranging, $W = P t$ : a 2 kW motor running for 30 s does $2000 \times 30 = 60000$ J of work. This is the link to energy bills, where energy in kW h $=$ power in kW $\times$ time in hours.

Power and Its Units: formulas and key facts

Power: $P = \frac{W}{t}$; W in joules, t in seconds, P in watts.
Power when lifting: $P = \frac{m g h}{t}$; h = vertical height.
Power at steady speed: $P = F v$; F along the motion; v in m/s.
Units of power: $1 W = 1 J s^{- 1} = 1 0^{7} erg s^{- 1}; 1 hp = 746 W$; kW = 10³ W, MW = 10⁶ W, GW = 10⁹ W.
Ratio of powers: $\frac{P _{1}}{P _{2}} = \frac{W _{1} / t _{1}}{W _{2} / t _{2}} = \frac{W _{1} t _{2}}{W _{2} t _{1}}$; Write the answer as a simplified whole-number ratio, in the order asked.

How to solve Power and Its Units questions

Most power numericals need the work first, then a division by time in seconds.

1Find the work: $W = F s$ , $W = m g h$ , or as given.
2Convert the time to seconds (minutes × 60, hours × 3600).
3Use $P = \frac{W}{t}$ , or $P = F v$ at steady speed.
4Convert the answer to kW, MW or hp if asked: divide by $1 0^{3}$ , $1 0^{6}$ or 746.
5For a comparison, compute both powers, write the ratio in the order asked and simplify.
6For energy from power, use $W = P t$ .

Power and Its Units in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Who is more powerful on the stairs?

Suppose two students race up the same flight of stairs, which rises 9 m. Anu (50 kg) takes 15 s; Bhavesh (60 kg) takes 20 s. ( $g = 10 m s^{- 2}$ )

Find each one's power. Who is more powerful?

Try it first, then show the solutionSolution

Anu: $P = \frac{50 \times 10 \times 9}{15} = 300$ W.
Bhavesh: $P = \frac{60 \times 10 \times 9}{20} = 270$ W.

Answer: Anu, 300 W against 270 W, though Bhavesh did more work.

Memory hook: More work is not more power; faster work is.

Horsepower to watts and energy

Imagine a 1.5 hp water pump on a farm runs for 2 hours.

Find its power in watts and the electrical energy it uses in kW h, assuming it draws its rated power.

Try it first, then show the solutionSolution

$P = 1.5 \times 746 = 1119$ W $= 1.119$ kW.
Energy $= 1.119 kW \times 2 h = 2.238$ kW h.

Answer: 1119 W; about 2.24 kW h.

Memory hook: hp × 746 gives watts; kW × hours gives units.

Tricks to remember Power and Its Units

Short memory aids. Say each one aloud once, then use it on a question the same day.

Power is pace
Power is how fast work is done: work per second.
Use it when: Definitions and comparisons.
Horse = 746
One horse, 746 watts: 'seven-four-six, the horse's tricks'.
Use it when: hp conversions.
kW vs kW h
kW is a speed (rate); kW h is a distance (amount). Rate × time = amount.
Use it when: Avoiding power/energy unit mix-ups.
Ratio in the asked order
First named, first written: 'Sumit to Amit' means P_Sumit : P_Amit, simplified to whole numbers.
Use it when: Comparison questions like 2024 Q2(v).

Power and Its Units: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Power of a motor · 1 mark · MCQBoard level

A motor does 4500 J of work in 1.5 minutes. Its power is:
(a) 3000 W
(b) 50 W
(c) 6750 W
(d) 0.83 W

Try it first, then show the solutionSolution

$t = 1.5 \times 60 = 90$ s.
$P = \frac{4500}{90} = 50$ W.

Answer: (b) 50 W

Example 2: Converting units of power · 2 marks · Short answerBoard level

Express (a) 3 hp in kW, (b) 2.5 MW in W.

Try it first, then show the solutionSolution

(a) $3 \times 746 = 2238$ W $= 2.238$ kW. (1)
(b) $2.5 \times 1 0^{6}$ W. (1)

Answer: (a) 2.238 kW (b) $2.5 \times 1 0^{6}$ W

Example 3: Comparing two powers · 3 marks · Short answerHarder board level

Riya lifts a 30 kg load through 4 m in 12 s. Sam lifts a 45 kg load through the same height in 24 s. Find the ratio of Riya's power to Sam's. ( $g = 10 m s^{- 2}$ )

Try it first, then show the solutionSolution

Riya: $P_{R} = \frac{30 \times 10 \times 4}{12} = 100$ W. (1)
Sam: $P_{S} = \frac{45 \times 10 \times 4}{24} = 75$ W. (1)
$P_{R} : P_{S} = 100 : 75 = 4 : 3$ . (1)

Answer: 4 : 3

Example 4: Power at steady speed · 3 marks · Short answerHarder board level

A cyclist rides at a steady 5 m/s against a total resistance of 40 N.
(a) Find the power the cyclist develops.
(b) Find the work done in 10 minutes.

Try it first, then show the solutionSolution

At steady speed the cyclist's forward force equals the resistance, 40 N. (½)
(a) $P = F v = 40 \times 5 = 200$ W. (1½)
(b) $W = P t = 200 \times 600 = 1.2 \times 1 0^{5}$ J. (1)

Answer: (a) 200 W (b) $1.2 \times 1 0^{5}$ J

Example 5: Choosing a pump · 3 marks · Short answerHOTS / competency

A pump must lift 1200 kg of water every minute into a tank 15 m above it. Only 60% of the motor's power ends up as work on the water. ( $g = 10 m s^{- 2}$ )
(a) Find the power delivered to the water.
(b) Find the power the motor must have.
(c) Express (b) in hp.

Try it first, then show the solutionSolution

(a) Work per minute $= 1200 \times 10 \times 15 = 1.8 \times 1 0^{5}$ J; $P = \frac{1.8 \times 1 0 ^{5}}{60} = 3000$ W. (1)
(b) $0.6 \times P_{motor} = 3000$ , so $P_{motor} = 5000$ W. (1)
(c) $\frac{5000}{746} \approx 6.7$ hp. (1)

Answer: (a) 3000 W (b) 5000 W (c) About 6.7 hp

Example 6: Case study: an escalator · 4 marks · Case-basedHOTS / competency

An escalator in a mall carries 20 people, each of mass 50 kg, every minute, up a vertical height of 6 m at steady speed. ( $g = 10 m s^{- 2}$ )
(a) Find the work done on the people in one minute.
(b) Find the power used to lift them, in kW and in hp.
(c) If it runs like this for one hour, how much energy does lifting them need, in kW h?

Try it first, then show the solutionSolution

(a) $W = 20 \times 50 \times 10 \times 6 = 6 \times 1 0^{4}$ J. (1)
(b) $P = \frac{6 \times 1 0 ^{4}}{60} = 1000$ W $= 1$ kW. (1)
In hp: $\frac{1000}{746} \approx 1.34$ hp. (1)
(c) $1 kW \times 1 h = 1$ kW h. (1)

Answer: (a) $6 \times 1 0^{4}$ J (b) 1 kW, about 1.34 hp (c) 1 kW h

Where students lose marks in Power and Its Units

The slips examiners see most often, and what to write instead.

Mistake: Leaving the ratio unsimplified or reversed
A comparison should be a whole-number ratio in the order named in the question.
Wrong working
$P_{1} : P_{2} = 1 : \frac{1}{4}$ , or $1 : 4$ when the first named is more powerful.
Right working
$P_{1} : P_{2} = 4 : 1$ .
Do this: Write $P_{1} = \dots$ , $P_{2} = \dots$ , then the ratio, simplified, first named first.
Usually costs: Reported for 2024 Q2(v), where candidates also multiplied instead of dividing.
Mistake: Dividing by minutes
Watts need seconds.
Wrong working
$P = \frac{600}{10} = 60$ W for 600 J in 10 minutes.
Right working
$P = \frac{600}{600} = 1$ W.
Do this: Convert time to seconds on a separate line.
Usually costs: The answer mark.
Mistake: Treating kW h as a unit of power
kW h is energy; kW is power.
Wrong working
The motor's power is 2 kW h.
Right working
The motor's power is 2 kW; in 3 hours it uses 6 kW h.
Do this: Power × time = energy.
Usually costs: Unit marks in MCQs and conversions.
Mistake: Using 1 hp = 1000 W
1 hp is 746 W.
Wrong working
5 hp $= 5000$ W.
Right working
5 hp $= 3730$ W.
Do this: Learn 746 as a fixed number.
Usually costs: The answer mark.

Exam tips

The 2024 paper expected the working $P_{1} : P_{2} = \frac{600}{10 \times 60} : \frac{300}{20 \times 60}$ and the answer $4 : 1$ ; show the conversion of minutes to seconds.
State the definition precisely: 'Power is the rate of doing work. P = W/t. SI unit: watt.'
When a body moves at steady speed, the driving force equals the resistance; then use $P = F v$ .
Give the answer in the unit asked: W, kW, MW or hp.

Practice questions on Power and Its Units

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
One watt is equal to:
(a) 1 J s
(b) 1 J s⁻¹
(c) 1 N s
(d) 1 J m⁻¹
Hint
Power = work ÷ time.
Answer
(b) 1 J s⁻¹
Q2 · 2 marks · Short answerBoard level
A girl of mass 55 kg runs up a staircase of vertical height 6 m in 11 s. Find the work she does against gravity and her power. ( $g = 10 m s^{- 2}$ )
Hint
$W = m g h$ , then divide by $t$ .
Answer
$W = 55 \times 10 \times 6 = 3300$ J; $P = \frac{3300}{11} = 300$ W.
Q3 · 2 marks · Short answerHarder board level
A does 900 J of work in 3 minutes; B does 400 J of work in 40 s. Find the ratio of the power of A to that of B.
Hint
Convert 3 minutes to seconds first.
Answer
$P_{A} = \frac{900}{180} = 5$ W; $P_{B} = \frac{400}{40} = 10$ W; $P_{A} : P_{B} = 1 : 2$ .
Q4 · 2 marks · Short answerHarder board level
A car's engine delivers 30 kW while the car moves at a steady 15 m/s on a level road. Find the total resistance to the car's motion.
Hint
$P = F v$ .
Answer
$F = \frac{P}{v} = \frac{30 000}{15} = 2000$ N.
Q5 · 2 marks · Short answerHarder board level
Express (a) 1 GW in horsepower, (b) $5 \times 1 0^{7}$ erg s⁻¹ in watts.
Hint
$1 hp = 746$ W; $1 W = 1 0^{7}$ erg s⁻¹.
Answer
(a) $\frac{1 0 ^{9}}{746} \approx 1.34 \times 1 0^{6}$ hp. (b) 5 W.
Q6 · 3 marks · Short answerHarder board level
A 2 kW motor runs for 30 s and all its work goes into lifting a 300 kg load at steady speed. Through what height is the load lifted? ( $g = 10 m s^{- 2}$ )
Hint
$W = P t$ , then $h = \frac{W}{m g}$ .
Answer
$W = 2000 \times 30 = 60000$ J; $h = \frac{60 000}{300 \times 10} = 20$ m.
Q7 · 4 marks · Long answerHOTS / competency
Crane X lifts 1000 kg through 10 m in 20 s. Crane Y lifts 1500 kg through 8 m in 30 s. ( $g = 10 m s^{- 2}$ ) (a) Which crane does more work? (b) Which is more powerful? (c) Find the ratio of their powers, X : Y.
Hint
Work and power can rank the cranes differently.
Answer
(a) $W_{X} = 1.0 \times 1 0^{5}$ J, $W_{Y} = 1.2 \times 1 0^{5}$ J: Y does more work. (b) $P_{X} = 5000$ W, $P_{Y} = 4000$ W: X is more powerful. (c) $5 : 4$ .

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Power of a machine doing 1000 J in 10 s?Show answer
100 W.
2.2 hp in watts?Show answer
1492 W.
3.How many watts in 1 MW?Show answer
$1 0^{6}$ W.
4.Is kW h a unit of power or energy?Show answer
Energy.
5.Power of a force of 50 N moving a body at 2 m/s in its direction?Show answer
100 W ( $P = F v$ ).

Power and Its Units: frequently asked questions

What is the difference between work and power?

Work is the amount of energy transferred by a force (in joules). Power is how fast that work is done, the work per second (in watts).

How many watts is one horsepower?

1 hp = 746 W. Multiply horsepower by 746 to get watts.

When can I use P = Fv?

When a constant force F acts along the motion of a body moving at steady speed v, for example an engine pulling a car at constant speed against resistance.