Question

图中表示一架实验飞机在一次飞行中，已飞行距离（英里）与经过时间（小时）的关系。在哪一个小时内，这架飞机的平均速度最大？

The graph relates the distance traveled (in miles) to the time elapsed (in hours) on a trip taken by an experimental airplane. During which hour was the average speed of this airplane the largest?

第一个小时 $(0\text{-}1)$

first $(0\text{-}1)$

第二个小时 $(1\text{-}2)$

second $(1\text{-}2)$

第三个小时 $(2\text{-}3)$

third $(2\text{-}3)$

第九个小时 $(8\text{-}9)$

ninth $(8\text{-}9)$

最后一个小时 $(11\text{-}12)$

last $(11\text{-}12)$

答案：B

知识点：数据与图表解读斜率

难度评级：970

解答：

任意一个小时内的平均速度等于这一个小时内飞行的距离，也就是图上对应一小时区间的竖直上升量。因此最大平均速度出现在曲线最陡的一小时。

从 $t=1$ 到 $t=2$ ，曲线从约 $500$ 英里升到约 $1000$ 英里，上升约 $500$ 英里，平均速度约 $500$ 英里每小时。其他小时的上升量都小于约 $350$ 英里。所以最大平均速度出现在第二个小时。

正确答案是 B。

The average speed during any single hour equals the distance the airplane covers in that hour, which on the graph is the vertical rise of the curve over that one-hour interval. So the largest average speed happens during the hour where the curve is steepest.

From $t=1$ to $t=2$ the curve climbs from about $500$ miles to about $1000$ miles, a rise of roughly $500$ miles, giving an average speed near $500$ mph. During every other hour the curve rises by less than $350$ miles, so those average speeds are all smaller. The steepest climb, and hence the largest average speed, is during the second hour.

Thus, the correct answer is B .

1990 AMC 8 第 23 题

答案：B

难度评级：970

解答：

其他年份的第 23 题