直线运动(高考真题汇编)

直线运动

1 .（6分）甲乙两辆汽车在平直的公路上沿同一方向作直线运动，t =0时刻同时经过公路旁的同一个路标。在描述两车运动的v －t 图中（如图），直线a 、b 分别描述了甲乙两车在0~20秒的运动情况。关于两车之间的位置关系，下列说法正确的是（）

A.在0~10秒内两车逐渐靠近

B.在10~20秒内两车逐渐远离

C.在5~15秒内两车的位移相等

D.在t =10秒时两车在公路上相遇

【解析】在0－10 s 内，乙车的速度一直比甲车大，两车应逐渐远离，则A 不正确；在10－20 s 内，甲车的速度一直比乙车大，两车逐渐靠近，则B 不正确；在5－15 s 内，两图象与坐标轴的面积相等，则两车的位移相等，则C 正确；在t ＝10 s 时两车速度相等，相距最远，则D 不正确，所以正确答案为C 。

【答案】：C

2 .（6分）甲乙两车在公路上沿同一方向做直线运动，它们的v －t 图象如图所示．两图象在t ＝t 1时相交于P 点，P 在横轴上的投影为Q ，ΔOPQ 的面积为S ．在t ＝0时刻，乙车在甲车前面，相距为d ．已知此后两车相遇

两次，且第一次相遇的时刻为t ′，则下面四组t ′和d 的组合

可能是（）

A ．t ′＝t 1，d ＝S

B ．S d ,t t 4

1211==' C ．S d ,t t 21211==' D ．S d ,t t 43211==' 【解析】本题考查追及相遇问题。在t 1时刻如果甲车没有追上乙车，以后就不可能追上了，故t′ ＜t ，A 错；从图像中甲、乙与坐标轴围成的面积即对应的位移看，甲在t 1时间内运动的位移比乙的多S ，当t′ =0.5 t 1时，甲的面积比乙的面积多出3 S /4，即相距d =3 S /4，选项D

正确。此类问题要抓住图像的交点的

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