Kinetic energy exam questions with worked answers
By Mehmood Kakar · Updated
Quick answer
Every kinetic energy question uses Ek = ½mv². Convert mass to kg and speed to m/s, square the speed before multiplying, and take a square root when you are finding speed. The seven questions below cover each type you are likely to meet, from 2-mark substitutions to 5-mark questions that link kinetic and potential energy.
The method
Kinetic energy questions look different on the surface but follow the same four steps. Write the equation. Convert mass to kilograms and speed to metres per second. Substitute, squaring the speed before you multiply. Write the answer with the unit, joules.
If the question asks for speed or mass, rearrange first. The rearranging guide shows how. Each worked answer below follows the same four-line layout described in how to show your working.
Q1: Find kinetic energy
A car of mass 800 kg travels at 15 m/s. Calculate its kinetic energy. (2 marks)
- Ek = ½ m v²
- Ek = 0.5 × 800 × 15²
- 15² = 225, so Ek = 0.5 × 800 × 225
- Ek = 90,000 J
One mark for the substitution, one for the answer. Typing 0.5 × 800 × 15 and forgetting the square gives 6000 J, which scores only the substitution mark if it was written down.
Q2: Mass in grams
A tennis ball of mass 60 g is hit at 20 m/s. Calculate its kinetic energy. (3 marks)
- Ek = ½ m v²
- Convert: m = 60 g ÷ 1000 = 0.060 kg
- Ek = 0.5 × 0.060 × 20² = 0.5 × 0.060 × 400
- Ek = 12 J
Leaving the mass in grams gives 12,000 J. A tennis ball with that much energy would be more dangerous than most cars in a car park, so an answer like that should send you back to check your units.
Q3: Find speed
A cyclist and bike have a combined mass of 70 kg and 3150 J of kinetic energy. Calculate their speed. (3 marks)
- Rearrange: v = √(2Ek ÷ m)
- 2 × 3150 = 6300; 6300 ÷ 70 = 90
- v = √90 = 9.4868…
- v = 9.5 m/s (2 s.f.)
The common mistake is stopping at 90. That number is v², not v. A cyclist doing 90 m/s would be travelling at over 300 km/h.
Q4: Find mass
An object moving at 10 m/s has 2.5 kJ of kinetic energy. Calculate its mass. (3 marks)
- Rearrange: m = 2Ek ÷ v²
- Convert: Ek = 2.5 kJ × 1000 = 2500 J
- m = (2 × 2500) ÷ 10² = 5000 ÷ 100
- m = 50 kg
Q5: Speed in km/h
A car of mass 1200 kg travels at 72 km/h. Calculate its kinetic energy. (3 marks)
- Ek = ½ m v²
- Convert: v = 72 km/h ÷ 3.6 = 20 m/s
- Ek = 0.5 × 1200 × 20² = 0.5 × 1200 × 400
- Ek = 240,000 J (240 kJ)
To change km/h to m/s, divide by 3.6. Using 72 directly gives 3,110,400 J, nearly 13 times too big. The units guide explains where the 3.6 comes from.
Q6: Doubling the speed
The car in Q1 speeds up from 15 m/s to 30 m/s. Calculate its new kinetic energy and explain how it compares with the original. (3 marks)
- Ek = 0.5 × 800 × 30² = 0.5 × 800 × 900
- Ek = 360,000 J
- 360,000 ÷ 90,000 = 4
- The kinetic energy is 4 times bigger, because speed is squared: doubling v multiplies v² by 2² = 4.
Explanation marks need the reason, not just the number. "Because speed is squared" is the phrase examiners look for. This is also why stopping distances rise so steeply with speed.
Q7: A falling object
A 0.50 kg ball is dropped from a height of 3.2 m. Ignore air resistance. g = 9.8 N/kg. Calculate the speed of the ball just before it hits the ground. (5 marks)
- GPE lost: Ep = m g h = 0.50 × 9.8 × 3.2 = 15.68 J
- With no air resistance, all of this becomes kinetic energy: Ek = 15.68 J
- Rearrange: v = √(2Ek ÷ m) = √(2 × 15.68 ÷ 0.50)
- v = √62.72 = 7.9195…
- v = 7.9 m/s (2 s.f.)
This is the classic linked question. The key line is the second one: say that the GPE lost equals the kinetic energy gained. Keep 15.68 unrounded when you carry it into the second equation. The GPE exam questions page covers the first half in more depth.
Check any of these answers with the kinetic energy calculator. It shows the same steps.
Practice
Try these before opening the answers.
1. A 0.15 kg cricket ball is bowled at 30 m/s. Calculate its kinetic energy.
Ek = 0.5 × 0.15 × 30² = 0.5 × 0.15 × 900 → Ek = 67.5 J (68 J to 2 s.f.)
2. A 2.0 kg trolley has 9.0 J of kinetic energy. Calculate its speed.
v = √(2 × 9.0 ÷ 2.0) = √9.0 → v = 3.0 m/s
3. A 1500 kg van travels at 54 km/h. Calculate its kinetic energy.
v = 54 ÷ 3.6 = 15 m/s → Ek = 0.5 × 1500 × 15² = 0.5 × 1500 × 225 → Ek = 168,750 J (169,000 J to 3 s.f.)
Frequently asked questions
What is the kinetic energy equation?
Kinetic energy = 0.5 × mass × speed² (Ek = ½mv²). Kinetic energy is in joules (J), mass in kilograms (kg) and speed in metres per second (m/s).
How do I find speed from kinetic energy?
Rearrange to v = √(2Ek ÷ m). Multiply the kinetic energy by 2, divide by the mass, then take the square root.
What happens to kinetic energy if speed doubles?
It becomes four times bigger, because speed is squared in the equation. If speed triples, kinetic energy becomes nine times bigger.
How many marks are kinetic energy questions worth?
A straight substitution is usually 2 marks. Questions that need a unit conversion or rearranging are usually 3 marks, and questions that link two equations can be worth 4 or 5.