PhysicsICSE Class 8 · Energy

Kinetic and Potential Energy: KE = ½mv², PE = mgh and Energy Changes (ICSE Class 8)

Updated 17 October 2026 · Fact-checked

Kinetic energy is the energy of motion, KE = ½mv²; potential energy is stored energy, and for a raised body PE = mgh. Energy only changes form: for a freely falling body (no air), the PE lost equals the KE gained.

As the ball falls, blue PE shrinks and orange KE grows by the same amount, so the total bar length never changes.

Illustration drawn for QuestionBuddy.

Understand Kinetic Energy, Potential Energy and Energy Transformations

Kinetic energy (KE). The energy a body has because it is moving:

$KE = \frac{1}{2} m v^{2}$

with $m$ in kg and $v$ in m/s; the answer is in joules.

Double the mass: KE doubles.
Double the speed: KE becomes four times ( $v$ is squared); triple the speed gives nine times.
A body at rest has zero KE.

Potential energy (PE). Energy stored in a body because of its position or shape.

Gravitational PE of a body raised above the ground: $PE = m g h$ ( $g = 10$ m/s²).
Energy stored by change of shape: a stretched rubber band, a wound spring, a bent bow.

The higher and heavier the body, the greater its PE. PE depends on the height measured from a chosen level (usually the ground).

Energy transformations. Energy cannot be created or destroyed; it changes form.

Situation	Change
Falling ball	PE → KE
Torch	chemical → electrical → light (and heat)
Electric fan	electrical → kinetic (and some sound, heat)
Hydroelectric station	PE of water → KE → electrical
Solar cell	light → electrical
Burning fuel in an engine	chemical → heat → kinetic

A freely falling body (ignore air). The total of PE + KE stays the same. At the top it is all PE ( $m g h$ ); just before the ground it is all KE ( $\frac{1}{2} m v^{2}$ ). So the PE lost equals the KE gained, and at any height the sum is the same.

Bodies thrown upwards go the other way: KE decreases and PE increases until the body stops momentarily at the top.

Work and energy. The work done on a body is stored as energy: lifting a body stores $m g h$ as PE; the work done to speed it up appears as KE.

Kinetic Energy, Potential Energy and Energy Transformations: formulas and key facts

Kinetic energy: $KE = \frac{1}{2} m v^{2}$; m in kg, v in m/s.
Gravitational potential energy: $PE = m g h$; g = 10 m/s²; h from the ground.
Energy of a falling body: $m g h = \frac{1}{2} m v^{2}$; No air resistance: PE lost = KE gained.
Ratio rule: $v \to 2 v \Rightarrow KE \to 4 KE$; KE is proportional to the square of speed.

How to solve Kinetic Energy, Potential Energy and Energy Transformations questions

Choose KE or PE from what the body is doing, then use conservation for falling or thrown bodies.

1Moving body: use $\frac{1}{2} m v^{2}$ . Raised body: use $m g h$ .
2Keep mass in kg and speed in m/s; use $g = 10$ m/s².
3For free fall, write total energy at the top, then PE and KE at the point asked: their sum stays the same.
4To find speed from KE, rearrange: $v = \frac{2 KE}{m}$ .
5State the energy change in words (PE to KE and so on).

Kinetic Energy, Potential Energy and Energy Transformations 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.

Why the fast car is so dangerous

Suppose a 1000 kg car travels at 10 m/s and later at 20 m/s.

Find the KE at each speed and the extra energy the brakes must remove at the higher speed.

Try it first, then show the solutionSolution

At 10 m/s: $\frac{1}{2} \times 1000 \times 1 0^{2} = 50000$ J.
At 20 m/s: $\frac{1}{2} \times 1000 \times 2 0^{2} = 200000$ J, four times as much.
Extra energy $= 200000 - 50000 = 150000$ J.

Answer: 50 000 J and 200 000 J; the speed doubles but the KE becomes four times.

Memory hook: Double speed, quadruple energy.

Water in a hill tank

Imagine a tank on a hill holds 250 kg of water at a height of 12 m above a house.

Find the PE of the water and how long it could power a 100 W bulb if all of it became electrical energy (an ideal case).

Try it first, then show the solutionSolution

$PE = 250 \times 10 \times 12 = 30000$ J.
$t = \frac{30 000}{100} = 300$ s.

Answer: 30 000 J; 300 s (5 minutes) in the ideal case.

Memory hook: High water carries stored energy.

Tricks to remember Kinetic Energy, Potential Energy and Energy Transformations

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

Half-m-v-squared
"Half a mass times speed-squared": the square makes speed matter most.
Use it when: KE formula.
Mighty height
m, g, h: "Mighty Gravity Height" gives PE.
Use it when: PE formula.
Top all PE, bottom all KE
Falling ball: PE at the top turns into KE at the bottom.
Use it when: Energy conservation.

Kinetic Energy, Potential Energy and Energy Transformations: solved examples

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

Example 1: KE of a trolley · 1 mark · MCQBoard level

The kinetic energy of a 2 kg trolley moving at 3 m/s is:
(a) 3 J
(b) 6 J
(c) 9 J
(d) 18 J

Try it first, then show the solutionSolution

$KE = \frac{1}{2} \times 2 \times 3^{2} = 9$ J.

Answer: (c) 9 J

Example 2: PE of a flower pot · 2 marks · Short answerBoard level

A 5 kg pot is on a shelf 8 m above the ground. Find its potential energy. ( $g = 10$ m/s²)

Try it first, then show the solutionSolution

$PE = m g h$ (½)
$= 5 \times 10 \times 8 = 400$ J. (1½)

Answer: 400 J

Example 3: A dropped ball · 4 marks · Long answerHarder board level

A ball of mass 0.5 kg is dropped from a height of 20 m. Ignore air. Find (a) its PE at the top, (b) its KE just before landing, (c) its speed then, (d) its KE and PE at 10 m height. ( $g = 10$ m/s²)

Try it first, then show the solutionSolution

(a) $0.5 \times 10 \times 20 = 100$ J. (1)
(b) All of it becomes KE: 100 J. (1)
(c) $\frac{1}{2} \times 0.5 \times v^{2} = 100 \Rightarrow v^{2} = 400$ ; $v = 20$ m/s. (1)
(d) At 10 m: PE $= 0.5 \times 10 \times 10 = 50$ J; KE $= 100 - 50 = 50$ J. (1)

Answer: (a) 100 J (b) 100 J (c) 20 m/s (d) 50 J each

Example 4: Comparing kinetic energies of two bodies · 3 marks · Short answerHarder board level

Body A has mass m and speed 2v; body B has mass 2m and speed v. Find the ratio of their kinetic energies, KE_A : KE_B.

Try it first, then show the solutionSolution

$KE_{A} = \frac{1}{2} m (2 v)^{2} = 2 m v^{2}$ . (1)
$KE_{B} = \frac{1}{2} (2 m) v^{2} = m v^{2}$ . (1)
Ratio $= 2 : 1$ . (1)

Answer: 2 : 1

Example 5: Roller coaster · 4 marks · Case-basedHOTS / competency

A car of mass 400 kg is released from rest at the top of a track 25 m above the ground; ignore friction. (a) Find its total energy at the top. (b) Find its KE and speed at a point 5 m above the ground. (c) State the energy change from top to bottom. ( $g = 10$ m/s²)

Try it first, then show the solutionSolution

(a) $400 \times 10 \times 25 = 100000$ J. (1)
(b) PE at 5 m $= 400 \times 10 \times 5 = 20000$ J; KE $= 100000 - 20000 = 80000$ J. (1)
$\frac{1}{2} \times 400 \times v^{2} = 80000 \Rightarrow v^{2} = 400$ , $v = 20$ m/s. (1)
(c) PE changes to KE. (1)

Answer: (a) 100 000 J (b) 80 000 J, 20 m/s (c) PE to KE

Where students lose marks in Kinetic Energy, Potential Energy and Energy Transformations

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

Mistake: Not squaring the speed
KE depends on v².
Wrong working
" $KE = \frac{1}{2} \times 2 \times 3 = 3$ J."
Right working
" $KE = \frac{1}{2} \times 2 \times 3^{2} = 9$ J."
Do this: Square the speed first, then multiply.
Mistake: Forgetting the half
KE has a factor of one half.
Wrong working
" $KE = 2 \times 3^{2} = 18$ J."
Right working
" $KE = \frac{1}{2} \times 2 \times 9 = 9$ J."
Do this: Write the formula before substituting.
Mistake: Using speed doubling = KE doubling
Doubling speed gives four times the KE.
Wrong working
"Speed doubled, so KE doubled."
Right working
"Speed doubled, so KE became four times."
Do this: KE ∝ v²: say the power.

Exam tips

Write the formula (KE or PE), the substitution and the unit (J).
For falling bodies, say "PE lost = KE gained (ignoring air)".
Use g = 10 m/s² and state it.
Name the energy change in words for any device question.

Practice questions on Kinetic Energy, Potential Energy and Energy Transformations

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 · Very short answerBoard level
Name the main energy change in a hydroelectric power station.
Hint
Think of falling water.
Answer
Potential energy of stored water → kinetic energy → electrical energy.
Q2 · 3 marks · Short answerHarder board level
A cricket ball of mass 0.16 kg has 8 J of kinetic energy when it leaves the bat. Find its speed, and the new KE if the speed were halved.
Hint
Rearrange $\frac{1}{2} m v^{2}$ ; halving the speed gives a quarter.
Answer
$\frac{1}{2} \times 0.16 \times v^{2} = 8 \Rightarrow v^{2} = 100$ ; $v = 10$ m/s. At half the speed KE is $\frac{1}{4}$ : $2$ J.
Q3 · 2 marks · Short answerHarder board level
The speed of a moving body is tripled. By what factor does its KE change? If the original KE was 8 J, find the new value.
Hint
KE depends on the square of speed.
Answer
KE becomes $3^{2} = 9$ times; new KE $= 8 \times 9 = 72$ J.
Q4 · 3 marks · Short answerHarder board level
A 0.2 kg stone is thrown straight up at 15 m/s. Find its initial KE, the PE at the highest point and the maximum height. Ignore air. ( $g = 10$ m/s²)
Hint
KE at the start equals PE at the top.
Answer
KE $= \frac{1}{2} \times 0.2 \times 1 5^{2} = 22.5$ J. PE at the top $= 22.5$ J. $0.2 \times 10 \times h = 22.5 \Rightarrow h = 11.25$ m.
Q5 · 4 marks · Long answerHOTS / competency
Explain the energy changes when a boy on a swing goes from the highest point to the lowest point and then up the other side. Where is the KE greatest and where is the PE greatest? State what happens to the total if air resistance is ignored.
Hint
Track PE and KE through the swing.
Answer
At the highest point the swing is momentarily at rest: PE is greatest, KE is zero. Going down, PE changes to KE; at the lowest point KE is greatest and PE is least. Going up the other side, KE changes back to PE. Ignoring air resistance, the total energy stays the same.

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.Formula for KE?Show answer
½mv².
2.Formula for gravitational PE?Show answer
mgh.
3.Speed doubled: KE becomes?Show answer
Four times.
4.PE to KE example?Show answer
Falling ball.
5.Energy cannot be…?Show answer
Created or destroyed; only changed.

Kinetic Energy, Potential Energy and Energy Transformations: frequently asked questions

What is kinetic energy?

Kinetic energy is the energy of a moving body. It is calculated as ½mv², with mass in kg and speed in m/s, and measured in joules.

What is potential energy?

Potential energy is stored energy due to position or shape. A body of mass m raised through height h has gravitational potential energy mgh.

What happens to energy when a ball falls?

Its potential energy decreases and its kinetic energy increases by the same amount (ignoring air), so the total energy stays the same.