The formula for the change in kinetic energy ($\Delta KE$) is the final kinetic energy minus the initial kinetic energy.
Understanding Kinetic Energy
Kinetic energy is the energy that an object possesses due to its motion. Simply put, if an object is moving, it has kinetic energy.
The standard formula used to calculate the kinetic energy (KE) of an object is:
KE = ½ m v²
Where:
- KE is the kinetic energy (measured in Joules, J)
- m is the mass of the object (measured in kilograms, kg)
- v is the velocity of the object (measured in meters per second, m/s)
This formula highlights that kinetic energy depends directly on the mass of the object and the square of its velocity. A heavier object moving at the same speed has more kinetic energy than a lighter one, and doubling an object's speed quadruples its kinetic energy.
Calculating the Change in Kinetic Energy
The change in kinetic energy ($\Delta KE$) is calculated by finding the difference between the object's final kinetic energy and its initial kinetic energy.
According to the reference, to calculate the change in kinetic energy, "subtract the initial kinetic energy from the final kinetic energy."
This can be represented mathematically as:
$\Delta KE = KE{final} - KE{initial}$
Deriving the Change in Kinetic Energy Formula
Using the base formula for kinetic energy (KE = ½ m v²), we can write the formulas for the initial and final kinetic energy:
- Initial Kinetic Energy ($KE_{initial}$): $KE{initial} = ½ m v{initial}²$
- Final Kinetic Energy ($KE_{final}$): $KE{final} = ½ m v{final}²$
Substituting these into the formula for the change in kinetic energy ($\Delta KE = KE{final} - KE{initial}$), we get:
$\Delta KE = (½ m v{final}²) - (½ m v{initial}²)$
This formula can be factored to simplify it, assuming the mass (m) of the object remains constant:
$\Delta KE = ½ m (v{final}² - v{initial}²)$
This final formula is a very useful way to calculate the change in kinetic energy if you know the object's mass and its initial and final velocities.
Variables in the Change in KE Formula
Let's break down the variables in the formula $\Delta KE = ½ m (v{final}² - v{initial}²)$:
| Variable | Description | Units (SI) |
|---|---|---|
| $\Delta KE$ | Change in Kinetic Energy | Joules (J) |
| m | Mass of the object | Kilograms (kg) |
| $v_{initial}$ | Initial velocity of the object | Meters per second (m/s) |
| $v_{final}$ | Final velocity of the object | Meters per second (m/s) |
Practical Example
Imagine a car with a mass of 1500 kg accelerating from an initial velocity of 10 m/s to a final velocity of 20 m/s. To find the change in kinetic energy:
- Identify variables:
- m = 1500 kg
- $v_{initial}$ = 10 m/s
- $v_{final}$ = 20 m/s
- Apply the formula:
- $\Delta KE = ½ m (v{final}² - v{initial}²)$
- $\Delta KE = ½ 1500 kg ((20 m/s)² - (10 m/s)²)$
- $\Delta KE = 750 kg * (400 m²/s² - 100 m²/s²)$
- $\Delta KE = 750 kg * (300 m²/s²)$
- $\Delta KE = 225,000 J$
The change in kinetic energy of the car is 225,000 Joules, or 225 kJ.
Why is Change in KE Important?
The change in kinetic energy is a fundamental concept in physics, particularly linked to the Work-Energy Theorem. This theorem states that the net work done on an object by external forces is equal to the change in its kinetic energy. Understanding $\Delta KE$ helps analyze how forces affect an object's motion and energy state.
