一辆汽车沿平直公路从甲站开往乙站,起动时的加速度为2m/s2,加速行驶5s后,匀速行驶2min,然后刹车,滑 一辆汽车沿着平直公路从甲站开往乙站,起步阶段的加速度为2m/...

\u4e00\u8f86\u6c7d\u8f66\u6cbf\u5e73\u76f4\u516c\u8def\u4ece\u7532\u7ad9\u51fa\u53d1\u5f00\u5f80\u4e59\u7ad9\uff0c\u8d77\u52a8\u52a0\u901f\u5ea6\u4e3a2m/s2\uff0c\u52a0\u901f\u884c\u9a765\u79d2\uff0c\u540e\u5300\u901f\u884c\u9a762\u5206\u949f\uff0c\u7136\u540e\u5239\u8f66\u505a

\uff081\uff09\u6c7d\u8f66\u505a\u5300\u52a0\u901f\u8fd0\u52a8\u65f6\u7684\u52a0\u901f\u5ea6a=2m/s2\uff0c\u52a0\u901f\u8fd0\u52a8\u7684\u65f6\u95f4\u4e3a5s\uff0c\u5219\u6c7d\u8f66\u5728\u5300\u52a0\u901f\u8fc7\u7a0b\u4e2d\u7684\u4f4d\u79fbx1\uff1d12at2\uff1d12\u00d72\u00d752m\uff1d25m\u6839\u636e\u901f\u5ea6\u65f6\u95f4\u5173\u7cfb\u53ef\u77e5\uff0c\u52a0\u901f5s\u540e\u6c7d\u8f66\u7684\u901f\u5ea6v=at=2\u00d75m/s=10m/s\uff0c\u5219\u6c7d\u8f66\u5728\u5300\u901f\u8fd0\u52a82\u5206\u949f\u65f6\u95f4\u5185\u7684\u4f4d\u79fbx2=vt=10\u00d7120m=1200m\u6c7d\u8f66\u505a\u5300\u51cf\u901f\u8fd0\u52a8\u7684\u4f4d\u79fbx3=50m\u6240\u4ee5\u7532\u4e59\u4e24\u7ad9\u95f4\u7684\u8ddd\u79bbx=x1+x2+x3=25+1200+50m=1275m\uff082\uff09\u6c7d\u8f66\u505a\u5300\u51cf\u901f\u8fd0\u52a8\u7684\u521d\u901f\u5ea6v0=10m/s\uff0c\u672b\u901f\u5ea6v=0\uff0c\u4ea7\u751f\u7684\u4f4d\u79fbx3=50m\u5219\u6839\u636e\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u7684\u5e73\u5747\u901f\u5ea6\u516c\u5f0f\u77e5\uff0c\u5300\u51cf\u901f\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\u7684\u5e73\u5747\u901f\u5ea6.v3\uff1dv+v02\uff1d0+102m/s\uff1d5m/s\u6240\u4ee5\u5300\u51cf\u901f\u8fd0\u52a8\u8fc7\u7a0b\u65f6\u95f4t3\uff1dx3.v3\uff1d505s\uff1d10s\u6240\u4ee5\u6c7d\u8f66\u4ece\u7532\u81f3\u4e59\u6240\u7528\u65f6\u95f4t=t1+t2+t3=5+120+10s=135s\u5219\u6c7d\u8f66\u4ece\u7532\u5230\u4e59\u7684\u5e73\u5747\u901f\u5ea6.v\uff1dxt\uff1d1275135m/s\u22489.4m/s\u7b54\uff1a\uff081\uff09\u7532\u4e59\u4e24\u7ad9\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e3a1275m\uff0e\uff082\uff09\u6c7d\u8f66\u4ece\u7532\u7ad9\u5230\u4e59\u7ad9\u7684\u5e73\u5747\u901f\u5ea6\u4e3a9.4m/s\uff0e

\uff081\uff09\u52a0\u901f5s\u540e\u7684\u901f\u5ea6\u4e3a\uff1av\uff1da1t 1\uff1d10m/s\u5300\u51cf\u901f\u8fc7\u7a0b\u7684\u521d\u901f\u5ea6\u4e3a10m/s\uff0c\u672b\u901f\u5ea6\u4e3a\u96f6\uff0c\u7531\uff1avt2?v22a\uff1ds3\uff0c\u5f97\uff1aa=-1m/s2\u5300\u51cf\u901f\u8fc7\u7a0b\u7684\u52a0\u901f\u5ea6\u5927\u5c0f\u4e3a1m/s2\uff0c\u65b9\u5411\u4e0e\u521d\u901f\u5ea6\u65b9\u5411\u76f8\u53cd\uff082\uff09\u5300\u51cf\u901f\u8fc7\u7a0b\uff1avt=v+at3\uff0c\u5f97\uff1at3=10s\uff0c\u4ece\u7532\u7ad9\u5230\u4e59\u7ad9\u7684\u65f6\u95f4\u4e3a\uff1at=t1+t2+t3=5+120+10=135s\uff083\uff09\u5300\u52a0\u901f\u8fc7\u7a0b\uff1as1\uff1d12a1t12\uff1d25m\u5300\u901f\u8fc7\u7a0b\uff1as2=vt2=10\u00d7120=1200m\u5168\u8fc7\u7a0b\uff1as=s1+s2+s3=1275m\u5168\u8fc7\u7a0b\u7684\u5e73\u5747\u901f\u5ea6\u5927\u5c0f\u4e3a\uff1a.v\uff1dst\uff1d1275135\uff1d9.4m/s\u7b54\uff1a\uff081\uff09\u5300\u51cf\u901f\u8fc7\u7a0b\u7684\u52a0\u901f\u5ea6\u5927\u5c0f1m/s2\uff1b\uff082\uff09\u4ece\u7532\u7ad9\u8fd0\u52a8\u5230\u4e59\u7ad9\u7684\u65f6\u95f4\u662f135s\uff1b\uff083\uff09\u4ece\u7532\u7ad9\u5230\u4e59\u7ad9\u7684\u5e73\u5747\u901f\u5ea6\u5927\u5c0f\u662f9.4m/s\uff0e

匀加速运动的末速度v=a1t1=2×5m/s=10m/s,
匀加速运动的位移x1
1
2
a1t12
1
2
×2×25m=25m

匀速的位移x2=vt2=10×120m=1200m,
则甲乙两站的距离x=x1+x2+x3=25+1200+50m=1275m.
根据x3
v
2
t3
得,匀减速运动的时间t3
2x3
v
2×50
10
s=10s

则汽车从甲站到乙站的时间t=t1+t2+t3=5+120+10s=135s.
答:甲、乙两站的距离为1275m,汽车从甲站到乙站的时间为135s.

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