Kinetic Energy Formula
The kinetic energy formula KE = ½mv² calculates the energy of a moving object.
Learn how mass and velocity affect kinetic energy with examples.
The Formula
KE = ½mv²
Kinetic energy is the energy an object possesses due to its motion. It increases with the square of velocity, so doubling the speed quadruples the energy.
Variables
| Symbol | Meaning |
|---|---|
| KE | Kinetic energy (measured in joules, J) |
| m | Mass of the object (measured in kilograms, kg) |
| v | Velocity of the object (measured in meters per second, m/s) |
Example 1
A 70 kg runner is sprinting at 8 m/s. What is their kinetic energy?
Identify the values: m = 70 kg, v = 8 m/s
Apply the formula: KE = ½mv² = ½ × 70 × 8²
KE = ½ × 70 × 64 = 35 × 64
KE = 2,240 J
Example 2
A 0.15 kg baseball has 135 J of kinetic energy. How fast is it moving?
Rearrange: v² = 2 × KE / m
v² = 2 × 135 / 0.15 = 270 / 0.15 = 1,800
v = √1,800
v ≈ 42.4 m/s
When to Use It
Use the kinetic energy formula to calculate the energy of moving objects.
- Determining the energy of vehicles, projectiles, or athletes in motion
- Energy conservation problems (converting between KE and PE)
- Calculating the work needed to bring an object to a certain speed
- Comparing energy at different speeds
Key Notes
- Velocity is squared: Doubling an object's speed quadruples its kinetic energy. This is why high-speed collisions are so much more destructive — crash energy grows as the square of velocity.
- KE is a scalar quantity: Kinetic energy has no direction. Two objects moving in opposite directions at the same speed have the same KE, even though their momenta cancel.
- Work-energy theorem: The net work done on an object equals its change in kinetic energy: W_net = ΔKE = KE_final − KE_initial. This connects force, displacement, and kinetic energy in one relationship.
- Relationship to momentum: KE = p²/(2m), where p = mv is momentum. At the same momentum, a lighter object has more kinetic energy. At the same KE, a heavier object has more momentum.
- Relativistic correction: At speeds approaching the speed of light, KE = (γ − 1)mc², where γ = 1/√(1 − v²/c²). The classical formula KE = ½mv² is accurate to within 1% for speeds below about 14% of the speed of light.