Power Examples: 44 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Power.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The rate at which work is done or energy is transferred, measured in watts (joules per second).

How fast you use or produce energy. A powerful engine does work quickly.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Power asks what energy enters, leaves, stays stored, or changes form in the chosen system.

Common stuck point: Students often know a formula related to power but skip the recognition step: Can I define the system and track energy before and after the interaction or process? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Can I define the system and track energy before and after the interaction or process?

Worked Examples

Example 1

easy

A motor does

6000 \text{ J}

of work in

30 \text{ s}

. What is the power output?

Answer

P = 200 W

First step

Use the power formula:

P = \frac{W}{t}

Full solution

2
Substitute the values: $P = \frac{6000}{30}$ .
3
$P = 200 W$

Power is the rate of doing work or transferring energy. It tells us how quickly energy is used, not just how much.

Example 2

medium

70 \text{ kg}

person runs up a

5 \text{ m}

staircase in

4 \text{ s}

. What is the power output? Use

g = 9.8 \text{ m/s}^2

Example 3

medium

60 \text{ kg}

runner climbs

4 \text{ m}

of vertical stairs in

5 \text{ s}

(

g = 9.8

). Find her average power output against gravity.

Example 4

medium

2.5 \text{ kW}

heater runs for

30 \text{ minutes}

. How much energy (in joules) does it use?

Example 5

hard

A river flows at

200 \text{ kg/s}

down a

25 \text{ m}

vertical drop. A turbine captures the energy at

60\%

efficiency (

g = 9.8

). Find the electrical power output.

Example 6

hard

A wind turbine intercepts

400 \text{ m}^2

of wind at

10 \text{ m/s}

(air density

1.225 \text{ kg/m}^3

). At

40\%

efficiency, find the electric power output. The kinetic energy flux of the wind is

\tfrac{1}{2}\rho A v^3

Example 7

challenge

A constant force does

W = 9000 \text{ J}

of work over

30 \text{ s}

on an object whose average speed during that interval is

5 \text{ m/s}

. Find the average power and the average force.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

100 \text{ W}

light bulb is on for

2 \text{ hours}

. How much energy does it use?

Example 2

medium

Two cranes each lift a

500 \text{ kg}

load

20 \text{ m}

. Crane A takes

50 \text{ s}

and Crane B takes

100 \text{ s}

easy

A pump does

1500 \text{ J}

of work in

5 \text{ s}

. What is its power output?

Example 24

easy

A constant horizontal force of

25 \text{ N}

moves a cart at

4 \text{ m/s}

. Find the instantaneous power delivered.

Example 25

easy

Which is more powerful: doing

200 \text{ J}

10 \text{ s}

150 \text{ J}

5 \text{ s}

Example 26

easy

Two motors deliver the same

5000 \text{ J}

but motor A takes

25 \text{ s}

and motor B takes

10 \text{ s}

. Find each motor's power.

Example 27

medium

20 \text{ kW}

car engine drives the car at

25 \text{ m/s}

on level ground. Find the driving force.

Example 28

medium

An elevator lifts a

400 \text{ kg}

load at a constant

1.5 \text{ m/s}

(

g = 9.8

). Find the motor's power output (against gravity).

Example 29

medium

0.75 \text{ kW}

winch lifts a

50 \text{ kg}

crate at constant speed (

g = 9.8

). Find the lifting speed.

Example 30

medium

A pump lifts

120 \text{ kg}

of water

10 \text{ m}

40 \text{ s}

(

g = 9.8

). Find the average power required (ignore losses).

Example 31

medium

An athlete delivers

1.2 \text{ kJ}

to a barbell in

0.8 \text{ s}

. Find the average power.

Example 32

medium

Two cyclists climb the same hill. Cyclist A delivers

250 \text{ W}

for

8 \text{ minutes}

; cyclist B delivers

300 \text{ W}

for

7 \text{ minutes}

. Which did more work?

Example 33

medium

200 \text{ W}

pump runs

15 \text{ minutes}

. Express the energy used in kilojoules.

Example 34

medium

1200 \text{ kg}

car accelerates from rest to

20 \text{ m/s}

10 \text{ s}

. Ignoring friction, find the average power delivered.

Example 35

hard

1000 \text{ kg}

car climbs a

5\%

grade (5 m rise per 100 m) at constant

20 \text{ m/s}

(

g = 9.8

). Find the engine power against gravity alone.

Example 36

hard

70 \text{ kg}

cyclist climbs a hill rising

80 \text{ m}

at a steady

150 \text{ W}

of useful power (

g = 9.8

). Ignoring friction, find the climb time.

Example 37

challenge

1500 \text{ kg}

car accelerates from

10 \text{ m/s}

30 \text{ m/s}

8 \text{ s}

on level ground. Find the average power delivered (ignoring friction and drag).

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Related Concepts

Work Energy Electrical Power

Background Knowledge

These ideas may be useful before you work through the harder examples.

workenergy