Kinetic and Gravitational Potential Energy
Two formulae and one principle — energy is conserved. Most lost marks here come from a single omission: forgetting to square the velocity.
1. Kinetic energy
Kinetic energy is the energy an object has because of its MOTION.
KE = ½ m v² kinetic energy (J) = ½ × mass (kg) × velocity² (m/s)²
Example: a 1200 kg car at 20 m/s.
- KE = ½ × 1200 × 20² = ½ × 1200 × 400 = 240 000 J
SQUARE THE VELOCITY. This is the single most common error in the topic, and it was recorded repeatedly — one calculation gave 500 000 J where 10 000 J was correct, purely from mishandling v².
Square only the velocity, not the mass, and remember the ½.
A consequence worth knowing:
Doubling the speed QUADRUPLES the kinetic energy, because v is squared. Trebling it multiplies KE by nine.
This is why stopping distances grow so sharply with speed, and it is a favourite exam point.
Kinetic energy is never negative, because v² is always positive — even for an object moving backwards.
A stationary object has zero kinetic energy — but during a jump, an object is only momentarily stationary at the very top. A recorded confusion was over whether KE could be zero during a jump: it is zero only at the highest point (for vertical motion), not throughout.
2. Gravitational potential energy
GPE is the energy an object has because of its HEIGHT in a gravitational field.
GPE = m g h = mass (kg) × gravitational field strength (N/kg) × height (m)
Example: a 50 kg object lifted 3 m, with g = 9.8.
- GPE = 50 × 9.8 × 3 = 1470 J
Use the CHANGE in height when a question asks for the change in GPE. Measuring from the wrong reference point was a recorded error — what matters is how far it rose or fell.
Use the value of g the question gives — 9.8, 9.81 or 10.
Mass in kilograms, height in metres. Converting grams to kilograms, and millimetres or centimetres to metres, were both recorded errors.
3. Energy conversion
Energy cannot be created or destroyed, only transferred from one store to another.
A falling object
As it falls: GPE → KE.
GPE lost = KE gained (ignoring air resistance) m g h = ½ m v²
The masses cancel, giving:
v = √(2 g h)
Example: an object dropped from 20 m, with g = 10.
- v = √(2 × 10 × 20) = √400 = 20 m/s
The mass cancels, so all objects reach the same speed from the same height without air resistance — a heavy ball and a light one land together.
Other conversions
| Situation | Conversion |
|---|---|
| Object thrown upwards | KE → GPE |
| Pendulum swinging down | GPE → KE |
| Pendulum swinging up | KE → GPE |
| Stretched spring released | elastic PE → KE |
| Compressing a spring | KE → elastic PE |
| Falling with air resistance | GPE → KE + thermal |
Get the direction of the conversion right. Confusing which way energy flows between kinetic and elastic potential was a recorded error. Ask: what is the object gaining? A falling object gains speed, so it gains KE.
At the top of a pendulum swing, GPE is maximum and KE is zero. At the lowest point, KE is maximum and GPE is minimum.
With air resistance, some energy becomes thermal energy in the surroundings, so the object arrives with less KE than the GPE it lost. Energy is still conserved — it has just gone somewhere less useful.
4. Method for calculations
- Write the formula
- Convert units — kg, m, m/s
- Substitute, squaring v where required
- Give the answer in joules with the right significant figures
Check units before substituting — tutors flagged this directly, and it is where most errors originate.
For conversion questions, set energy before = energy after and solve.
5. Mistakes that cost marks
Forgetting to square the velocity.
Squaring the mass instead of the velocity.
Omitting the ½ in KE.
Leaving mass in grams, or height in cm or mm.
Using the wrong value of g.
Using absolute height instead of the change.
Reversing the direction of an energy conversion.
Forgetting energy lost to air resistance when a question mentions it.
Confusing KE with GPE.
Omitting the unit — energy is in joules.
Frequently asked questions
What is kinetic energy? The energy of an object due to its motion: KE = ½mv².
What is gravitational potential energy? The energy due to an object’s height: GPE = mgh.
What happens to KE if the speed doubles? It becomes four times greater, because v is squared.
What is the unit of energy? The joule (J).
What happens as an object falls? GPE is converted to KE.
How do I find the speed of a falling object? Set mgh = ½mv²; the mass cancels, giving v = √(2gh).
Do heavy objects fall faster? No — the mass cancels, so without air resistance they reach the same speed.
Where is KE greatest for a pendulum? At the lowest point. GPE is greatest at the highest point.
What if there is air resistance? Some energy becomes thermal energy, so the object has less KE than the GPE lost — but total energy is still conserved.
Can kinetic energy be negative? No — v² is always positive.
Quick revision checklist
- I know KE = ½mv² and always square v
- I know doubling speed quadruples KE
- I know GPE = mgh
- I use the change in height
- I convert mass to kg and lengths to m
- I use the value of g given
- I know energy is conserved
- I can equate GPE lost to KE gained
- I know the mass cancels, so v = √(2gh)
- I can state the conversion for falls, throws, pendulums and springs
- I know where KE and GPE are greatest on a pendulum
- I can account for air resistance as thermal energy
- I give answers in joules
These notes cover kinetic and gravitational potential energy in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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