The kinetic energy, in joules, of an object with mass 9 kilograms traveling at a speed

Choice A is correct. It's given that the kinetic energy, in joules, of an object with a mass of $9$ kilograms traveling at a speed of $v$ meters per second is given by the function $K$, where $K\left(v\right)=\frac{9}{2}{v}^2$. It follows that in the equation $K\left(34\right)=\mathrm{5,202}$, $34$ is the value of $v$, or the speed of the object, in meters per second, and $\mathrm{5,202}$ is the kinetic energy, in joules, of the object at that speed. Therefore, the best interpretation of $K\left(34\right)=\mathrm{5,202}$ in this context is the object traveling at $34$ meters per second has a kinetic energy of $\mathrm{5,202}$ joules.

Choice B is incorrect. The object traveling at $340$ meters per second has a kinetic energy of $\mathrm{520,200}$ joules.

Choice C is incorrect. The object traveling at $\mathrm{5,202}$ meters per second has a kinetic energy of $\mathrm{121,773,618}$ joules.

Choice D is incorrect. The object traveling at $\mathrm{23,409}$ meters per second has a kinetic energy of $\mathrm{2,465,915,764.5}$ joules.