问题 计算题

汽车的加速性能用车的速度从0到100 km/h(按30 m/s估算)的加速时间来表示,这个时间越短,汽车启动时的加速性能就越好。下表列出了两种汽车的性能指标。

现让甲、乙两车在同一条平直公路上同向行驶,乙车在前,甲车在后,两车相距85 m。甲车先启动,经过一段时间t0乙车再启动。若两车从静止启动后均以各自的最大加速度匀加速运动,在乙车开出8 s时两车相遇,则

(1)t0应该满足的条件是什么?在此条件下,两车相遇时甲车行驶的路程是多少?

(2)以乙车刚刚启动时为t=0时刻,在同一个坐标系内画出甲、乙两车从乙车启动到两车相遇过程中的vt图像。

答案

解:(1)首先确定两车相遇前各自的运动情况,是都在匀加速运动,还是一个匀加速运动一个匀速运动,还是都在匀速运动

甲车的加速度为a1=2.5 m/s2

加速到速度最大时所需时间t1=16 s

乙车的加速度为a2=5 m/s2

加速到速度最大时所需时间t2=10 s

乙车开动8 s时两车相遇,相遇时乙车发生的位移x2a2t2=160 m

甲车发生的位移应为x1x2x0=245 m

甲车由速度为零加速到最大速度发生的位移x=320 m

因为x>x1,所以两车相遇时两车都是处于加速阶段,故有a1(t0t)2x0a2t2

解得t0=6 s,两车相遇时甲车行驶的路程是x1a1(t0t)2=245 m

(2)当乙车刚启动时,甲车的速度v1a1t0=15 m/s

两车相遇时甲车的速度v2a1(t0t)=35 m/s

vt图像如图所示

阅读理解

In a room at Texas Children Cancer Center in Houston, eight-year-old Simran Jatar lay in bed with a drip (点滴) above her to fight her bone cancer. Over her bald (秃的) head, she wore a pink hat that matched her clothes. But the third grader’s cheery dressing didn’t mask her pain and weary eyes.

Then a visitor showed up. “Do you want to write a song?” asked Anita Kruse, 49, rolling a cart equipped with an electronic keyboard, a microphone and speakers. Simran stared. “Have you ever written a poem?” Anita Kruse continued. “Well, yes,” Simran said.

Within minutes, Simran was reading her poem into the microphone. “Some bird soaring through the sky,” she said softly. “Imagination in its head…” Anita Kruse added piano music, a few warbling (鸣, 唱) birds, and finally the girl’s voice. Thirty minutes later, she presented Simran with a CD of her first recorded song.

That was the beginning of Anita Kruse’s project, Purple Songs Can Fly, one that has helped more than 125 young patients write and record songs. As a composer and pianist who had performed at the hospital, Kruse said that the idea of how she could help “came in one flash”.

The effect on the kids has been great. One teenage girl, curling (蜷缩) in pain in her wheelchair, stood unaided to dance to a hip-hop song she had written. A 12-year-old boy with Hodgkin’s disease who rarely spoke surprised his doctors with a song he called I Can Make It.

“My time with the kids is heartbreaking because of the severity of their illnesses,” says Anita Kruse. “But they also make you happy, when the children are smiling, excited to share their CD with their families.”

Simran is now an active sixth grader and cancer-free. From time to time, she and her mother listen to her song, Always Remembering, and they always remember the “really sweet and nice and loving” lady who gave them a shining moment in the dark hour.

小题1:Simran Jatar lay in bed in hospital because ______.

A.most of her hair had fallen out

B.she was receiving treatment for cancer

C.she felt depressed and quit from school

D.she was suffering from a pain in her back小题2:What do we know about Anita Kruse’s project?

A.It helps young patients record songs.

B.It is supported by singers and patients.

C.It aims to replace the medical treatment.

D.It offers patients chances to realize their dreams.小题3:What does the case of a 12-year-old boy suggest?

A.Most children are naturally fond of music.

B.He was brave enough to put up performance.

C.The project has positive effect on young patients.

D.Singing is the best way to treat some illnesses.小题4:What is probably the best title for the passage?

A.Purple Songs Can Fly

B.Singing Can Improve Health

C.A Shining Moment in Life

D.A Kind Woman—Anita Kruse

单项选择题