Practice kinetic energy problems with step-by-step solutions. Learn how to use KE = 1/2mv squared to solve real physics problems.
Practice makes perfect with kinetic energy problems. The formula is always the same: KE = 1/2mv squared. You just plug in the numbers and calculate. These problems start easy and get harder. Each one has a full solution so you can check your work.
| Problem Type | What You Need | What You Find |
|---|---|---|
| Basic KE | Mass and velocity | Kinetic energy |
| Find mass | KE and velocity | Mass in kg |
| Find velocity | KE and mass | Speed in m/s |
| Compare | Two objects | Which has more KE |
| Word problem | Real scenario | Apply the formula |
Problem 1: Rolling Ball
A 3 kg ball rolls across the floor at 4 m/s. How much kinetic energy does it have?
Solution: KE = 1/2 x 3 x (4 x 4) KE = 1/2 x 3 x 16 KE = 1/2 x 48 KE = 24 J
The ball has 24 joules of kinetic energy.
Problem 2: Running Dog
A 15 kg dog runs at 5 m/s. What is its kinetic energy?
Solution: KE = 1/2 x 15 x (5 x 5) KE = 1/2 x 15 x 25 KE = 1/2 x 375 KE = 187.5 J
The dog has 187.5 joules of kinetic energy.
Problem 3: Flying Bird
A 2 kg bird flies at 12 m/s. Calculate its kinetic energy.
Solution: KE = 1/2 x 2 x (12 x 12) KE = 1/2 x 2 x 144 KE = 1/2 x 288 KE = 144 J
The bird has 144 joules of kinetic energy.
Sometimes you know the kinetic energy and velocity. You need to find the mass. Rearrange the formula: m = 2KE / v squared.
Problem 4: Unknown Mass
An object has 100 J of kinetic energy at 10 m/s. What is its mass?
Solution: m = 2 x 100 / (10 x 10) m = 200 / 100 m = 2 kg
The object has a mass of 2 kilograms.
Problem 5: Heavy Object
A moving object has 500 J of KE at 5 m/s. Find its mass.
Solution: m = 2 x 500 / (5 x 5) m = 1,000 / 25 m = 40 kg
The object has a mass of 40 kilograms.
Problem 6: Light Object
An object has 50 J of KE at 20 m/s. What is its mass?
Solution: m = 2 x 50 / (20 x 20) m = 100 / 400 m = 0.25 kg
The object has a mass of 0.25 kilograms, or 250 grams.
You can also find velocity when you know KE and mass. The formula is v = square root of (2KE / m).
Problem 7: Find the Speed
A 4 kg object has 200 J of kinetic energy. How fast is it moving?
Solution: v squared = 2 x 200 / 4 v squared = 400 / 4 v squared = 100 v = 10 m/s
The object is moving at 10 meters per second.
Problem 8: Fast Ball
A 0.15 kg baseball has 30 J of KE. What is its velocity?
Solution: v squared = 2 x 30 / 0.15 v squared = 60 / 0.15 v squared = 400 v = 20 m/s
The baseball is moving at 20 meters per second.
Problem 9: Slow Object
A 50 kg object has 25 J of KE. Find its speed.
Solution: v squared = 2 x 25 / 50 v squared = 50 / 50 v squared = 1 v = 1 m/s
The object is moving at 1 meter per second.
These problems use simple numbers. You can solve them with basic math.
Problem 10: Marble
A 0.1 kg marble rolls at 2 m/s. Find the KE.
KE = 1/2 x 0.1 x (2 x 2) KE = 1/2 x 0.1 x 4 KE = 1/2 x 0.4 KE = 0.2 J
Problem 11: Toy Car
A 0.5 kg toy car moves at 3 m/s. Find the KE.
KE = 1/2 x 0.5 x (3 x 3) KE = 1/2 x 0.5 x 9 KE = 1/2 x 4.5 KE = 2.25 J
Problem 12: Tennis Ball
A 0.06 kg tennis ball is served at 30 m/s. Find the KE.
KE = 1/2 x 0.06 x (30 x 30) KE = 1/2 x 0.06 x 900 KE = 1/2 x 54 KE = 27 J
These problems require more steps. Take your time.
Problem 13: Comparison
Object A has mass 6 kg and velocity 3 m/s. Object B has mass 3 kg and velocity 6 m/s. Which has more kinetic energy?
Object A: KE = 1/2 x 6 x (3 x 3) KE = 1/2 x 6 x 9 KE = 27 J
Object B: KE = 1/2 x 3 x (6 x 6) KE = 1/2 x 3 x 36 KE = 54 J
Object B has twice the kinetic energy, even with half the mass. The higher speed (squared) makes the difference.
Problem 14: Speeding Up
A 1,200 kg car goes from 10 m/s to 20 m/s. How much does its KE change?
At 10 m/s: KE = 1/2 x 1,200 x 100 = 60,000 J
At 20 m/s: KE = 1/2 x 1,200 x 400 = 240,000 J
Change = 240,000 - 60,000 = 180,000 J
The KE increased by 180,000 joules. That is four times the original amount.
Problem 15: Work and KE
A 70 kg cyclist does 1,400 J of work to speed up. If she started at 2 m/s, what is her final speed?
First find initial KE: KEi = 1/2 x 70 x 4 = 140 J
Add the work: KEf = 140 + 1,400 = 1,540 J
Find final speed: v squared = 2 x 1,540 / 70 v squared = 3,080 / 70 v squared = 44 v = 6.63 m/s
Her final speed is about 6.6 meters per second.
Problem 16: Braking
A 1,500 kg truck brakes from 25 m/s to 5 m/s. How much KE is removed?
At 25 m/s: KE = 1/2 x 1,500 x 625 = 468,750 J
At 5 m/s: KE = 1/2 x 1,500 x 25 = 18,750 J
Removed = 468,750 - 18,750 = 450,000 J
The brakes removed 450,000 joules. That energy turned into heat.
Problem 17: Rocket
A 10,000 kg rocket accelerates from 2,000 m/s to 8,000 m/s. How much kinetic energy does it gain?
At 2,000 m/s: KE = 1/2 x 10,000 x 4,000,000 = 20,000,000,000 J
At 8,000 m/s: KE = 1/2 x 10,000 x 64,000,000 = 320,000,000,000 J
Gain = 320 billion - 20 billion = 300 billion J
Problem 18: Two Objects with Same KE
A 4 kg object moves at 10 m/s. A 1 kg object has the same KE. How fast is the 1 kg object moving?
KE of 4 kg object: KE = 1/2 x 4 x 100 = 200 J
Find v for 1 kg object: v squared = 2 x 200 / 1 v squared = 400 v = 20 m/s
The 1 kg object must go twice as fast to have the same kinetic energy.
Mistake 1: Forgetting to square velocity first. Always do v x v before multiplying by mass. Order matters.
Mistake 2: Using wrong units. Mass must be in kg. Speed must be in m/s. If you have grams, divide by 1,000 first.
Mistake 3: Forgetting the 1/2. The formula is KE = 1/2mv squared, not KE = mv squared. That 1/2 is important.
Mistake 4: Mixing up mass and weight. Weight is measured in newtons. Mass is measured in kilograms. Use kilograms.
Mistake 5: Using speed instead of velocity. For KE calculations, velocity is the same as speed. Just use the number.
Discussion Questions
Classroom Activity: KE Race
Give students different objects with known masses. Have them roll the objects down a ramp and measure the speed at the bottom. Then calculate the KE for each. Rank them from least to most KE.
Common Misconceptions
Some students think the 1/2 in the formula is optional. It is not. It comes directly from the physics of acceleration.
Some students think KE and momentum are the same. They are related but different. Momentum is mv. KE is 1/2mv squared.
Last updated: June 15, 2026
A 4 kg object moves at 5 m/s. What is its KE?
If you triple the speed, KE increases by how much?
A 10 kg object has 80 J of KE. What is its velocity?
Two objects have the same KE. Object A has twice the mass of Object B. What does this tell you about their speeds?
A car doubles its speed from 10 m/s to 20 m/s. Its KE goes from 50,000 J to what?
Answers: B: 50 J, C: 9 times, B: 4 m/s, B: B is faster, C: 200,000 J
How do you solve kinetic energy problems?
Write down the mass and velocity, square the velocity, multiply by mass, then divide by 2. Always check your units are in kg and m/s.
What is a simple kinetic energy problem?
A 2 kg ball rolls at 3 m/s. KE = 1/2 x 2 x 3 squared = 1/2 x 2 x 9 = 9 J. The ball has 9 joules of kinetic energy.
How does mass affect answers in kinetic energy problems?
Mass has a direct effect. If you double the mass, the answer doubles. If you cut the mass in half, the answer is cut in half too.
How does speed affect kinetic energy in problems?
Speed is squared, so small changes in speed make big changes in the answer. Double the speed and the answer is four times bigger.
What units must you use in kinetic energy problems?
Mass must be in kilograms (kg) and velocity in meters per second (m/s). The answer will be in joules (J).
