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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

v=152-9.8t

A volcanologist modeling a volcanic eruption determines that vertical velocity, v, in meters per second (m/s), of the debris reaching the highest altitude t seconds after the eruption can be given by the equation above. Which of the following is the best interpretation of 152 in this context?

A.The velocity changed by 152 m/s every second.
B.The highest altitude reached by debris was 152 meters.
C.The debris hit the ground 152 seconds after the eruption.
D.The debris had a vertical velocity of 152 m/s at the time of eruption.

答案和解析

答案：D

解析：

Choice D is correct. To begin, write the equation in slope-intercept form: v=–9.8t+152.

In this equation the slope of v with respect to t is –9.8, and the v-intercept is 152.

Because the v-intercept is 152, the value of v is 152 when t is 0. By the definitions of v and t, the vertical velocity of the debris at the time of eruption was 152m/s.

The debris had a vertical velocity of 152m/s at the time of eruption.