The amount of work done by a body before coming to rest is known as it's kinetic energy .It's formula is =>1/2 mv^2. That's all.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. It is a scalar quantity and depends on the mass and velocity of the object. The formula for kinetic energy is:

Kinetic Energy (KE) = 1/2 * mass * velocity^2

Where:
- KE is the kinetic energy of the object in joules (J)
- mass is the mass of the object in kilograms (kg)
- velocity is the velocity of the object in meters per second (m/s)

Explanation:

1. What is Kinetic Energy?
- Kinetic energy is the energy an object possesses due to its motion.
- It is a form of mechanical energy, which is the sum of an object's potential energy and kinetic energy.

2. Formula for Kinetic Energy
- The formula for kinetic energy is KE = 1/2 * mv^2, where m is the mass of the object and v is its velocity.
- The mass is a measure of an object's inertia, and the velocity represents the speed and direction of its motion.
- The square of the velocity in the formula emphasizes the significance of the object's speed.
- The 1/2 factor is included to ensure that the formula aligns with the work-energy principle.

3. Derivation of the Formula
- The derivation of the kinetic energy formula involves the principles of work and energy.
- Work (W) is defined as the force (F) applied on an object multiplied by the displacement (d) in the direction of the force.
- By applying Newton's second law (F = ma), it can be derived that the work done on an object is equal to the change in its kinetic energy.
- Mathematically, W = ΔKE = F * d = m * a * d = m * (dv/dt) * d = m * v * (dv/dt) * d
- Simplifying the equation further, we get W = m * v * dv
- Integrating both sides of the equation, we obtain the formula for kinetic energy: KE = 1/2 * m * v^2

4. Units and Measurement
- Kinetic energy is measured in joules (J), which is a derived unit in the International System of Units (SI).
- The mass is measured in kilograms (kg), and the velocity is measured in meters per second (m/s).

In conclusion, kinetic energy is the energy possessed by an object due to its motion. The formula, KE = 1/2 * mass * velocity^2, quantifies this energy based on the mass and velocity of the object. Understanding kinetic energy is crucial in various fields, such as physics, engineering, and sports, as it helps explain and analyze the motion of objects.