Understanding Kinetic Energy

Kinetic energy (KE) is the energy an object possesses due to its motion. It's calculated using the following formula:

KE = (1/2) * m * v²

where:

* KE is kinetic energy

* m is mass

* v is velocity

Solving the Problem

1. Kinetic Energy of Body 1:

KE₁ = (1/2) * m * v²

2. Kinetic Energy of Body 2:

KE₂ = (1/2) * m * (2v)² = (1/2) * m * 4v²

3. Ratio of Kinetic Energies:

KE₁ / KE₂ = [(1/2) * m * v²] / [(1/2) * m * 4v²]

KE₁ / KE₂ = 1 / 4

Answer:

The ratio of the kinetic energies of the two bodies is 1:4. This means the body moving with twice the velocity has four times the kinetic energy of the body moving with the lower velocity.