To find the correct equation that relates kinetic energy (KE), mass (m), and velocity (v), let's consider each option one by one.
The general form of the equation for kinetic energy is derived from physical principles and has a specific structure.
Option A: [tex]\( KE = \frac{1}{2} m^2 v \)[/tex]
- This equation suggests that kinetic energy is proportional to the square of the mass, which is not consistent with the principles of kinetic energy in classical mechanics.
Option B: [tex]\(KE = \frac{1}{2} m v^2 \)[/tex]
- This equation suggests that kinetic energy is proportional to the mass and the square of the velocity, which is the correct and widely accepted form of the kinetic energy equation.
Option C: [tex]\( KE = \frac{1}{2} m v \)[/tex]
- This equation suggests that kinetic energy is proportional to the mass and the velocity, but not squared. This does not align with the traditional understanding of kinetic energy.
Option D: [tex]\( KE = \frac{1}{2} m v^3 \)[/tex]
- This equation suggests that kinetic energy is proportional to the mass and the cube of the velocity. This is not correct based on the standard physics formulation.
Given these considerations, the correct equation that appropriately relates kinetic energy, mass, and velocity is indeed:
Option B: [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
