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Advanced Math / Nonlinear functions Difficulty: Medium

An object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?

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Explanation

Choice A is correct. It’s given that an object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. This relationship can be represented by the equation $K equals, one half m v squared$ , where K is the kinetic energy, m is the mass, and v is the speed. Substituting a mass of 4 kilograms for m and a kinetic energy of 18 joules for K results in the equation $18 equals, one half times 4, times v squared$ , or $18 equals, 2 v squared$ . Dividing both sides of this equation by 2 yields $9 equals, v squared$ . Taking the square root of both sides yields $v equals, negative 3$ and $v equals 3$ . Since speed can’t be expressed as a negative number, the speed of the object is 3 meters per second.

Choice B is incorrect and may result from computation errors. Choice C is incorrect. This is the value of $v squared$ rather than v. Choice D is incorrect. This is the value of $4 v squared$ rather than v.