- Initial Kinetic Energy: Kinetic energy of a body is given by the formula \( KE = \frac{1}{2}mv^2 \), where m is the mass of the body and v is its velocity.
- Initial Velocity: Let's assume the initial velocity of the body is v.
- Initial Kinetic Energy: The initial kinetic energy of the body is \( KE = \frac{1}{2}mv^2 \).



- Doubled Velocity: If the velocity of the body is doubled, the new velocity becomes 2v.
- New Kinetic Energy: The new kinetic energy of the body after doubling its velocity is given by \( KE = \frac{1}{2}m(2v)^2 = 2(\frac{1}{2}mv^2) \).
- Comparison: Comparing the new kinetic energy with the initial kinetic energy, we find that the new kinetic energy is 4 times the initial kinetic energy.
- Impact: Doubling the velocity of a body increases its kinetic energy by a factor of 4.



- Effect on Kinetic Energy: When the velocity of a body is doubled, its kinetic energy increases significantly.
- Mathematical Explanation: This increase in kinetic energy is a result of the squared relationship between velocity and kinetic energy in the formula.
- Practical Example: For example, if a car's speed is doubled from 30 mph to 60 mph, its kinetic energy will increase by a factor of 4, leading to more energy being required to stop the car.
- Importance of Understanding: Understanding the relationship between velocity and kinetic energy is crucial in various fields such as physics, engineering, and transportation.