Question

甲、乙兩車從A地將一批物品勻速運(yùn)往B地，已知甲出發(fā)0.5h后乙開始出發(fā)，

如圖，線段OP、MN分別表示甲、乙兩車離A地的距離S（km）與時(shí)間t（h）的關(guān)

系，請(qǐng)結(jié)合圖中的信息解決如下問(wèn)題：

（1）求甲、乙兩車的速度；

（2）乙車到達(dá)B地后以原速立即返回．

①在圖中畫出乙車在返回過(guò)程中離A地的距離S（km）與時(shí)間t（h）的函數(shù)圖象，

并求出此時(shí)S與t的函數(shù)關(guān)系式．

②試求甲車在離B地多遠(yuǎn)處與返程中的乙車相遇?

Answer 1

解：（1）由題意可知M(0.5，0)，線段OP、MN都經(jīng)過(guò)（1.5，60）

甲車的速度60÷1.5＝40 km/小時(shí)，                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

乙車的速度60÷（1.5－0.5）＝60 km/小時(shí)，（2）①∵乙車到達(dá)B地，所用時(shí)間為180÷60＝3，所以點(diǎn)N的橫坐標(biāo)為3.5

乙車到達(dá)B地后以原速立即返回，到達(dá)A地，又經(jīng)過(guò)3小時(shí)，所以點(diǎn)Q的橫坐標(biāo)為6.5．

∴乙車在返回過(guò)程中離A地的距離S（km）與時(shí)間t（h）的函數(shù)圖象

為線段NQ．    ……4分

 法一：設(shè)S=kt+b，把（3.5，100），

3.5