PSAT Math Multiple-Choice Question 165: Answer and Explanation

Question: 165

A particle accelerates at a constant rate from a velocity of 20 meters per second to a velocity of 50 meters per second in 10 seconds. Which of the following expresses the velocity V, in meters per second, in terms of the time t, in seconds, after the acceleration began, for 0 ≤ t ≤ 10?

• A. V = -50 + 3t
• B. V = 20 + 3t
• C. V = -20 - 3t
• D. V = 50 - 3t

Correct Answer: B

Explanation:

B

The question asks for the velocity, in terms of t. There are variables in the answer choices, so plug in. According to the question, the particle accelerates from 20 to 50 meters per second in 10 seconds, so when t = 10, the velocity is 50. Let 50 be the target number, and plug t = 10 into each of the choices, eliminating any that are not equal to 50. Choice (A) is V = -50 + 3(10) = -20, so eliminate (A). Choice (B) is V = 20 + 3(10) = 50, so keep (B), but check the other answers just in case. Choice (C) is V = -20 - 3(10) = -50, so eliminate (C). Choice (D) is 50 - 3(10) = 20, so eliminate (D). The correct answer is (B).