identifying the equation for kinetic energy\nwhich is the correct equation for calculating the kinetic…

Brief Explanations:

Kinetic energy is the energy of motion. The formula for kinetic energy of an object with mass $m$ and velocity $v$ is $KE=\frac{1}{2}mv^{2}$. The formula $KE = mgh$ is for gravitational - potential energy, $KE=\frac{1}{2}at^{2}$ is not a correct kinetic - energy formula (it is related to displacement in uniformly - accelerated motion), and $KE=\frac{1}{4}g^{2}$ is also incorrect for kinetic energy.

Answer:

$KE=\frac{1}{2}mv^{2}$