Digital PSAT Math Practice Question 342: Answer and Explanation

Question: 342

The final velocity of a given object is expressed by the following formula:

\begin{matrix} Final velocity = \\ Initial velocity + Acceleration \times Time \end{matrix}

If a ball has an initial velocity of 4 m/s and a constant acceleration of 6 m/s², which inequality shows the range of times, T, that will cause the final velocity to have a value of at least 22 m/s?

A. T ≥ 3 seconds
B. T ≥ 8 seconds
C. 3 seconds ≤ T ≤ 5 seconds
D. 6 seconds ≤ T ≤ 22 seconds

Correct Answer: A

Explanation:

(A) Plug the given values into the equation:

\begin{array}{ccl} Final velocity & = & Initial velocity + Acceleration \times Time \\ Initial velocity = 4 m / s \\ Acceleration = 6 m / s^{2} \\ Final velocity = 22 m / s \end{array}

The final velocity must be at least 22 m/s. Set up the inequality so that the result for the final velocity could exceed 22 m/s:

\begin{array}{rcl} 22 & \leq & 4 + 6 T \\ 18 & \leq & 6 T \\ 3 & \leq & T \end{array}

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Digital PSAT Math Practice Question 342: Answer and Explanation

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