{"id":1407,"date":"2000-01-02T10:03:23","date_gmt":"2000-01-02T02:03:23","guid":{"rendered":"http:\/\/www.qiusir.cn\/archives\/1407"},"modified":"2026-09-15T13:22:04","modified_gmt":"2026-09-15T05:22:04","slug":"2%e5%8c%80%e5%8f%98%e9%80%9f%e7%9b%b4%e7%ba%bf%e8%bf%90%e5%8a%a8%e7%9a%84%e7%a0%94%e7%a9%b6","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=1407","title":{"rendered":"\u00a701-2.\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8"},"content":{"rendered":"

\"\"
\nvia[?<\/a>]
\n\u4e00\u822c\u6027\u7684\u5300\u53d8\u901f\u8fd0\u52a8\u4e2d\u95f4\u65f6\u523b\u7684\u4f4d\u7f6e\u4e0e\u8fd0\u884c\u4e2d\u70b9\u4f4d\u7f6e\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f$\\frac{1}{8}aT^2$\uff08\u56db\u79cd\u65b9\u6cd5\uff0c\u4ee3\u6570\u6cd5\u3001\u4e2d\u95f4\u65f6\u523b\u548c\u4e2d\u70b9\u901f\u5ea6\u516c\u5f0f\u3001\u56fe\u50cf\u5272\u8865\u4ee5\u53ca\u7b49\u5206\u82f9\u679c$\\frac{1}{2}a(\\frac{T}{2})^2$\uff09
\n\"\"
\np36\u7eb8\u5e26\u6cd5\u7ed8\u5236v-t\u56fe\u50cf\u3002
\n\u5bfc\u6570\u548c\u79ef\u5206\u7684\u95ee\u9898\u53ef\u4ee5\u7ed3\u5408\u5230a v s \u4e0a\u3002
\np44\u5149\u7535\u95e8\u7684\u5e94\u7528\u3002
\n\u5149\u7535\u95e8\u6d4b\u52a0\u901f\u5ea6\u8bef\u5dee\u5206\u6790\u3002\u6d4b\u91cf\u503c\u5927\u4e8e\u771f\u5b9e\u503c
\n$a=\\frac{(\\frac{d}{\\Delta t_1})^2+(\\frac{d}{\\Delta t_2})^2}{2L}$
\n\u9891\u95ea\u6444\u5f71<\/p>\n

\u76f8\u5bf9\u901f\u5ea6\u6bd4\u901f\u5ea6\u5408\u6210\u66f4\u751f\u6d3b\u5316\u3002<\/p>\n

a acceleration\u306e\u982d\u6587\u5b57
\n

\"\"<\/center><\/p>\n

\"\"<\/center><\/p>\n

\"\"<\/center><\/p>\n

\"\"<\/center>
\n\uff08\u516c\u5f0f\u589e\u52a0\u52a8\u80fd\u53d8\u4e3a\u4e00\u534a\uff08\u524d\u540e\u4e24\u4e2a\u8fc7\u7a0b\u5408\u5916\u529b\u7684\u529f\u4e00\u6837\uff09\u548c\u52a8\u91cf\u53d8\u4e3a\u4e00\u534a\uff08\u524d\u540e\u5408\u5916\u529b\u7684\u51b2\u91cf\u4e00\u6837\uff09\uff09
\n\uff08\u5b59\u6d5a\u8c6a\u6574\u7406\uff09\u8fd0\u52a8\u5b66\u516c\u5f0f\u6574\u7406\uff1a
\n
\"\"<\/center>
\n\u00b7\u57fa\u672c\u516c\u5f0f\uff1a
\n$\\bar{v} =\\frac{x}{t} $
\n$v=\\lim_{\\Delta t \\to 0} \\frac{\\Delta x}{\\Delta t} $
\n$v={x}’ \\left ( t \\right ) $
\n$a=\\lim_{\\Delta t \\to 0} \\frac{\\Delta v}{\\Delta t} $
\n$a={v}’ \\left ( t \\right ) ={x}” \\left ( t \\right ) $
\n$v=v_{0}+at$
\n$x=v_{0}\\cdot t+\\frac{1}{2} at^{2}$
\n$x=v_{t}\\cdot t-\\frac{1}{2}at^{2} $
\n$x=\\bar{v}\\cdot t=\\frac{v_{0}+v_{t}}{2} t$
\n$v_{t}^{2}-v_{0}^{2}=2ax$
\n$\\bar{v}=v_{\\frac{t}{2}} $
\n$\\bar{v}=\\frac{v_{0}+v_{t}}{2} $
\n$v_{\\frac{x}{2}}=\\sqrt{\\frac{v_{0}^{2}+v_{t}^{2}}{2} } $
\n\u4e24\u4e2a\u8fde\u7eed\u65f6\u95f4\u95f4\u9694T\u7684\u4f4d\u79fb\u5dee\uff1a$\\Delta x=aT^{2} $
\n\u7b2cn\u4e2aT\u4e0e\u7b2cm\u4e2aT\u7684\u4f4d\u79fb\u5dee\uff1a
\n$x_{n}-x_{m}=\\left ( n-m \\right )aT^{2} $
\n
\"\"<\/center>
\n\u00b7\u521d\u901f\u5ea6\u4e3a0\u7684\u5300\u52a0\u901f\u76f4\u7ebf\u8fd0\u52a8\uff1a
\n\u524dT\u65f6\u95f4\u5185\u4e2d\u95f4\u65f6\u523b\u4f4d\u7f6e\u4e0e\u4e2d\u95f4\u4f4d\u79fb\u7684\u8ddd\u79bb\uff1a$d=\\frac{1}{8}aT^{2} $
\n$T,2T,3T\\dots \\,nT$ \u65f6\u95f4\u672b\u7269\u4f53\u77ac\u65f6\u901f\u5ea6\u4e4b\u6bd4\uff1a
\n$v_{1T}:v_{2T}:v_{3T}: \\cdots :v_{nT}=1:2:3:\\cdots :n$
\n$T,2T,3T\\dots \\,nT$ \u65f6\u95f4\u5185\u7269\u4f53\u5e73\u5747\u901f\u5ea6\u4e4b\u6bd4\uff1a
\n$\\bar{v}_{1T}:\\bar{v}_{2T}:\\bar{v}_{3T}:\\cdots :\\bar{v}_{nT}=1:2:3:\\cdots :n$
\n$T,2T,3T\\dots \\,nT$ \u65f6\u95f4\u5185\u7269\u4f53\u4f4d\u79fb\u4e4b\u6bd4\uff1a
\n$x_{1T}:x_{2T}:x_{3T}: \\cdots :x_{nT}=1:4:9:\\cdots :n^{2}$
\n\u7269\u4f53\u901a\u8fc7$x,2x,3x\\dots \\,nx$ \u4f4d\u79fb\u672b\u77ac\u65f6\u901f\u5ea6\u4e4b\u6bd4\uff1a
\n$v_{1x}:v_{2x}:v_{3x}: \\cdots :v_{nx}=1:\\sqrt{2} :\\sqrt{3}:\\cdots :\\sqrt{n}$
\n\u7269\u4f53\u901a\u8fc7$x,2x,3x\\dots \\,nx$ \u4f4d\u79fb\u6240\u9700\u65f6\u95f4\u4e4b\u6bd4\uff1a
\n$t_{1x}:t_{2x}:t_{3x}: \\cdots :t_{nx}=1:\\sqrt{2} :\\sqrt{3}:\\cdots :\\sqrt{n}$
\n\u7269\u4f53\u901a\u8fc7$x,2x,3x\\dots \\,nx$ \u4f4d\u79fb\u8fc7\u7a0b\u5e73\u5747\u901f\u5ea6\u4e4b\u6bd4\uff1a
\n$\\bar{v}_{1x}:\\bar{v}_{2x}:\\bar{v}_{3x}: \\cdots :\\bar{v}_{nx}=1:\\sqrt{2} :\\sqrt{3}:\\cdots :\\sqrt{n}$
\n\u7269\u4f53\u7ecf\u8fc7\u8fde\u7eed\u76f8\u7b49\u65f6\u95f4\u5185\u4f4d\u79fb\u4e4b\u6bd4\uff1a
\n$x_{T_{1}}:x_{T_{2}}:x_{T_{3}}: \\cdots :x_{T_{n}}=1:3:5:\\cdots :\\left ( 2n-1\\right )$
\n\u7269\u4f53\u901a\u8fc7\u8fde\u7eed\u76f8\u7b49\u4f4d\u79fb\u6240\u9700\u65f6\u95f4\u4e4b\u6bd4\uff1a
\n$t_{x_{1}}:t_{x_{2}}:t_{x_{3}}:\\cdots:t_{x_{n}}=1:(\\sqrt{2}-1):(\\sqrt{3}-\\sqrt{2}):\\cdots :(\\sqrt{n}-\\sqrt{n-1}) $
\n\u9759\u6b62\u5f00\u59cb\uff0c\u7269\u4f53\u901a\u8fc7\u8fde\u7eed\u76f8\u7b49\u4f4d\u79fb\u5e73\u5747\u901f\u5ea6\u4e4b\u6bd4\uff1a
\n$1:\\sqrt{2}+1:\\sqrt{3}+\\sqrt{2}…\\sqrt{n}+\\sqrt{n-1}$
\n$x_n=v_0T-\\frac{1}{2}aT^2+naT^2$<\/p>\n

$v(t)=\\sqrt{v_0^2+2ax(t)}+v_0$<\/p>\n

$x(t)=\\frac{v(t)-v_0}{2}t+v_0t+x_0$\uff08\u4ece\u68af\u5f62\u9762\u79ef\u7684\u89d2\u5ea6\u8003\u8651\uff09
\n\u53e6\uff0c\u4e3a\u4e86\u66f4\u597d\u7406\u89e3$\\Delta x=aT^2$\uff0c\u7279\u522b\u8fdb\u884c\u4e86\u8868\u683c\u8bad\u7ec3\uff08\u5300\u53d8\u901f\u8fd0\u52a8\uff09…
\n

\"\"<\/center><\/p>\n

\u6709\u540c\u5b66\u505a\u9898\u76ee\u5584\u4e8e\u603b\u7ed3\u89c4\u5f8b
\n\u6bd4\u5982$\\frac{a_1}{a_2}=\\frac{1}{-3}$\u56de\u5230\u51fa\u53d1\u70b9\uff1b\u6bd4\u5982\u521d\u901f\u5ea6\u4e3a\u96f6\u7684\u5300\u52a0\u901f\uff0c\u6709$2:1:-\\frac{1}{8}$<\/p>\n

[?<\/a>]\u4e00\u9053\u8fd0\u52a8\u5b66\u9898\u76ee\u7684\u591a\u79cd\u89e3\u6cd5<\/p>\n","protected":false},"excerpt":{"rendered":"

via[?] \u4e00\u822c\u6027\u7684\u5300\u53d8\u901f\u8fd0\u52a8\u4e2d\u95f4\u65f6\u523b\u7684\u4f4d\u7f6e\u4e0e\u8fd0\u884c\u4e2d\u70b9\u4f4d\u7f6e\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f$\\frac{1}{8}aT^2$\uff08\u56db … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[5],"tags":[397,247,263],"class_list":["post-1407","post","type-post","status-publish","format-standard","hentry","category-physics","tag-g1","tag-physics","tag-teach"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/1407","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1407"}],"version-history":[{"count":2,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/1407\/revisions"}],"predecessor-version":[{"id":48965,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/1407\/revisions\/48965"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1407"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}