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Advanced Math / Nonlinear functions Difficulty: Easy

The kinetic energy, in joules, of an object with mass $9$ kilograms traveling at a speed of $v$ meters per second is given by the function $K$ , where $K (v) = \frac{9}{2} v^{2}$ . Which of the following is the best interpretation of $upper K left parenthesis 34 right parenthesis equals 5,202$ in this context?

The object traveling at $34$ meters per second has a kinetic energy of $5,202$ joules.

The object traveling at $340$ meters per second has a kinetic energy of $5,202$ joules.

The object traveling at $5,202$ meters per second has a kinetic energy of $34$ joules.

The object traveling at $23,409$ meters per second has a kinetic energy of $34$ joules.

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Explanation

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 $K (v) = \frac{9}{2} v^{2}$ . It follows that in the equation $upper K left parenthesis 34 right parenthesis equals 5,202$ , $34$ is the value of $v$ , or the speed of the object, in meters per second, and $5,202$ is the kinetic energy, in joules, of the object at that speed. Therefore, the best interpretation of $upper K left parenthesis 34 right parenthesis equals 5,202$ in this context is the object traveling at $34$ meters per second has a kinetic energy of $5,202$ joules.

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

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

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