1. The problem is to understand and explain the kinetic energy formula: $$E_k = \frac{1}{2} m v^2$$. 2. Here, $E_k$ represents the kinetic energy of an object, $m$ is the mass of the object, and $v$ is its velocity. 3. The formula states that kinetic energy is half the product of the mass and the square of the velocity. 4. This means if you know the mass and velocity of an object, you can calculate its kinetic energy by squaring the velocity, multiplying by the mass, and then taking half of that product. 5. For example, if an object has a mass of 2 kg and velocity of 3 m/s, its kinetic energy is: $$E_k = \frac{1}{2} \times 2 \times 3^2 = 1 \times 9 = 9$$ joules. 6. This formula is fundamental in physics for understanding the energy of moving objects.