问题 计算题

小汽车甲以8m/s的速度在平直的公路上向右匀速行驶。某时刻,发现在其正前方20m处,有一货车乙刚好以2m/s2的加速度由静止开始向右做匀加速直线运动,且当乙车速度达到12m/s时,便保持此速度匀速运动,而甲车继续匀速运动。

(1) 求乙车速度增加到8m/s所用的时间

(2)判断甲车能否追上乙车?若能追上,求出追上时所用的时间;若不能追上,求出甲、乙之间的最小距离

(3)请在图11中画出0~8s内甲、乙两车的速度v与时间t的图像

答案

(1)4s(2)追不上,最近距离4m(3)见答案解析

题目分析:(1)                

(2)乙车速度达到8m/Ss时,运动的位移大小为:

                    

此时,甲运动的位移大小为

                      

因为甲、乙运动的位移差为

             

所以,甲车不能追上乙车,且此时的距离就是最小距离

其最小距离为     

其它解法只有合理同样得分

(3)如图所示

 

点评:本题通过匀变速直线运动规律的相关公式求解追击问题,本题可以列出方程,通过数学一元二次方程的判别式计算的答案的个数。

单项选择题
单项选择题

In 1957 a doctor in Singapore noticed that hospitals were treating an unusual number of influenza-like cases. Influenza is sometimes called “flu” or a “bad cold”. He took samples from the throats of patients in his hospital and was able to find the virus of this influenza.

There are three main types of the influenza virus. The most important of these are types A and B, each of them having several sub-groups. With the instruments at the hospital the doctor recognized that the outbreak was due to a virus group A, but he did not know the sub-group. He reported the outbreak to the World Health Organization in Geneva. W. H.O. published the important news alongside reports of a similar outbreak in Hong Kong, where about 15%—20% of the population had become ill.

As soon as the London doctors received the package of throat samples, they began the standard tests. They found that by reproducing itself at very high speed, the virus had multiplied more than a million times within two days. Continuing their careful tests, the doctors checked the effect of drugs used against all the known sub-groups of virus type A. None of them gave any protection. This then, was something new: a new influenza virus against which the people of the world had no ready help whatsoever. Having isolated the virus they were working with, the two doctors now dropped it into the noses of some specially selected animals, which contact influenza in the same way as human beings do. In a short time the usual signs of the disease appeared. These experiments revealed that the new virus spread easily, but that it was not a killer. Scientists, like the general public, called it simply “Asian” flu.

The first discovery of the virus, however, was made in China before the disease had appeared in other countries. Various reports showed that the influenza outbreak started in China, probably in February of 1957. By the middle of March it had spread all over China. The virus was found by Chinese doctors early in March. But China was not a member of the World Health Organization and therefore did not report outbreaks of disease to it. Not until two months later, when travelers carried the virus into Hong Kong, from where it spread to Singapore, did the news of the outbreak reach the rest of the world. By this time it was started on its way around the world.

Thereafter, WHO’s Weekly Reports described the steady spread of this virus outbreak, which within four months swept through every continent.

The Singapore doctor found the influenza was caused by()

A. an influenza virus type

B.  a sub-group of virus type

C. a virus only existing in Asia.

D. a new type of influenza virus.