The given formula for kinetic energy $K$ is:

$K = \frac{1}{2} m v^2$

To solve for $m$ (mass) in terms of $K$ and $v$, follow these steps:

1. Start with the formula: $K = \frac{1}{2} m v^2$

2. Multiply both sides of the equation by 2 to eliminate the fraction: $2K = m v^2$

3. Solve for $m$ by dividing both sides by $v^2$ (since $v \neq 0$): $m = \frac{2K}{v^2}$

Thus, the mass $m$ in terms of the kinetic energy $K$ and the velocity $v$ is:

$m = \frac{2K}{v^2}$

Do you have any questions or would you like further details?

Here are 5 related questions to explore further:

1. How does kinetic energy change if the velocity of an object doubles?
2. If the mass of an object increases while its velocity remains constant, how does that affect its kinetic energy?
3. What is the kinetic energy of a 5 kg object moving at 10 m/s?
4. How would you derive the formula for velocity in terms of $K$ and $m$?
5. How does the kinetic energy formula relate to potential energy?

Tip: Kinetic energy depends quadratically on velocity, meaning that even small changes in velocity significantly affect the energy.