2001 AMC 8 第 19 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

19.

汽车 MM 以恒定速度行驶了一段给定时间,如虚线所示。汽车 NN 以两倍速度行驶相同距离。如果用实线表示汽车 NN 的速度和时间,哪张图表示这种情况?

Car MM traveled at a constant speed for a given time. This is shown by the dashed line. Car NN traveled at twice the speed for the same distance. If Car NN's speed and time are shown as a solid line, which graph illustrates this?

答案:D
知识点:路程、速度与时间数据与图表解读
难度评级:1430
解答:

汽车 NN 的速度是汽车 MM 的两倍,所以它在速度轴上的高度应是汽车 MM 的两倍。

因为汽车 NN 以更快速度行驶与汽车 MM 相同的距离,所以它用一半时间完成行程。

因此表示汽车 NN 速度的线段长度是表示汽车 MM 速度的线段长度的一半。

两条线都水平,因为速度恒定。查看给出的图,唯一满足条件的是图 D

所以正确答案是 D

Car NN travels at twice the speed of car M,M, so it is represented by a point that is twice as high on the speed axis as car M.M.

Since car NN travels at the same distance as car MM but at a faster speed, it takes half the time to complete the trip.

Therefore, the line representing car NN's speed is half the length of the line representing car MM's speed.

Both lines are horizontal because the speeds are constant. Examining the given graphs, the only one that meets these conditions is graph D .

Thus, D is the correct answer.

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