{"id":459,"date":"2023-09-02T12:49:38","date_gmt":"2023-09-02T04:49:38","guid":{"rendered":"http:\/\/ggapa.net:81\/?p=459"},"modified":"2023-10-15T00:18:29","modified_gmt":"2023-10-14T16:18:29","slug":"%e5%8c%80%e5%8f%98%e9%80%9f%e7%9b%b4%e7%ba%bf%e8%bf%90%e5%8a%a8%e5%b8%b8%e8%a7%81%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"http:\/\/ggapa.net:81\/2023\/09\/02\/%e5%8c%80%e5%8f%98%e9%80%9f%e7%9b%b4%e7%ba%bf%e8%bf%90%e5%8a%a8%e5%b8%b8%e8%a7%81%e5%85%ac%e5%bc%8f\/","title":{"rendered":"\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u5e38\u7528\u516c\u5f0f\u53ca\u63a8\u8bba"},"content":{"rendered":"<h1>\u901f\u67e5<\/h1>\n<p>$$V_t=V_0+at$$<\/p>\n<p>$$x=V_0t+\\frac{1}{2} at^2$$<\/p>\n<p>$$\\overline{v} =\\frac{V_0+V_t}{2} =V_{\\frac{t}{2} }$$<\/p>\n<p>$$x=\\frac{(V_0+V_t)t}{2} $$<\/p>\n<p>$$V_t^2-V_0^2=2ax$$<\/p>\n<p>$$V_\\frac{x}{2} =\\sqrt{\\frac{V_0^2+V_t^2}{2} }$$<\/p>\n<p>$$X_n-X_m=(n-m)at^2$$<\/p>\n<p>$$V_1:V_2:\\cdots:V_n=1:2:\\cdots:n$$<\/p>\n<p>$$x_1:x_2:\\cdots:x_n=1:4:\\cdots:n^2$$<\/p>\n<p>$$t_1:t_2:\\cdots:t_n = 1:(\\sqrt[]{2} -1):(\\sqrt[]{3}-\\sqrt[]{2}  ):\\cdots :(\\sqrt[]{n}-\\sqrt[]{n-1}  )$$<\/p>\n<h1>\u57fa\u672c\u516c\u5f0f<\/h1>\n<p>$V_t=V_0+at$<\/p>\n<p>$x=V_0t+\\frac{1}{2} at^2$<\/p>\n<p>$\\overline{v} =\\frac{V_0+V_t}{2} =V_{\\frac{t}{2} }$<\/p>\n<p>$x=\\frac{(V_0+V_t)t}{2} $<\/p>\n<h1>\u63a8\u8bba<\/h1>\n<p>$V_t^2-V_0^2=2ax$<\/p>\n<p>\u63a8\u5bfc\uff1a<\/p>\n<p>$$V_t^2-V_0^2=(V_0+at)^2-V_0^2=2V_0+a^2t^2=2a(V_0t+\\frac{1}{2}t^2 )=2ax$$<\/p>\n<hr \/>\n<p>$V_\\frac{x}{2} =\\sqrt{\\frac{V_0^2+V_t^2}{2} }$<\/p>\n<p>\u63a8\u5bfc\uff1a<\/p>\n<p>\u8bbe\u603b\u4f4d\u79fb\u4e3a $x$\uff0c\u7531\u516c\u5f0f $V_t^2-V_0^2=2ax$ \u53ef\u77e5\uff1a<\/p>\n<p>$$V_\\frac{x}{2}^2 -V_0^2=ax$$<\/p>\n<p>$$V_t^2-V_\\frac{x}{2} ^2=ax$$<\/p>\n<p>$$2V_\\frac{x}{2}^2 = V_0^2+V_t^2$$<\/p>\n<p>$$V_\\frac{x}{2} =\\sqrt{\\frac{V_0^2+V_t^2}{2} }$$<\/p>\n<hr \/>\n<p>$X_n-X_m=(n-m)at^2$\u5176\u4e2d(n\\ge m)$<\/p>\n<p>\u63a8\u5bfc\uff1a<br \/>\n\u7531\u516c\u5f0f $x=V_0t+\\frac{1}{2} at^2$ \u53ef\u77e5\uff1a<\/p>\n<ul>\n<li>\n<p>\u5f53$n=m+1$\u65f6\uff1a<\/p>\n<p>$$X_n=(V_m+at)t+\\frac{1}{2} at^2$$<\/p>\n<\/li>\n<\/ul>\n<p>$$X_m=V_mt+\\frac{1}{2} at^2$$<\/p>\n<p>$$X_n-X_m=V_mt+at^2+\\frac{1}{2} at^2-V_mt-\\frac{1}{2} at^2=at^2$$<\/p>\n<ul>\n<li>\u5f53$n \\ge m \u65f6\uff1a$<\/li>\n<\/ul>\n<p>$$X_n-X_m=(n-m)at^2$$<\/p>\n<hr \/>\n<p>\u5728\u521d\u901f\u5ea6\u4e3a $0$ \u7684\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u7684\u6761\u4ef6\u4e0b\uff0c\u516c\u5f0f\u9000\u5316\u4e3a\uff1a<\/p>\n<p>$V_t=at$<\/p>\n<p>$x=\\frac{1}{2}at^2$<\/p>\n<p>$V^2=2ax$<\/p>\n<p>\u5728\u524d$1\\cdot Ts,2\\cdot Ts,\\cdots ,n\\cdot Ts$ \u65f6\uff1a<\/p>\n<p>$$V_1:V_2:\\cdots:V_n=1:2:\\cdots:n$$<\/p>\n<p>$$x_1:x_2:\\cdots:x_n=1:4:\\cdots:n^2$$<\/p>\n<p>\u63a8\u5bfc\uff1a<\/p>\n<p>$$V_1:V_2:\\cdots:V_n=at:2at:\\cdots:nat=1:2:\\cdots:n$$<\/p>\n<p>$$x_1:x_2:\\cdots:x_n=\\frac{1}{2} at^2:\\frac{1}{2} a(2t)^2:\\cdots :\\frac{1}{2} a(nt)^2=1:4:\\cdots:n^2$$<\/p>\n<hr \/>\n<p>\u5728\u521d\u901f\u5ea6\u4e3a $0$ \u65f6\u7684\u5300\u53d8\u901f\u76f4\u7ebf\u8fd0\u52a8\u4e2d\uff0c\u6309\u7167\u4f4d\u79fb\u7b49\u5206\u65f6:<\/p>\n<p>$$t_1:t_2:\\cdots:t_n = 1:(\\sqrt[]{2} -1):(\\sqrt[]{3}-\\sqrt[]{2}  ):\\cdots :(\\sqrt[]{n}-\\sqrt[]{n-1}  )$$<\/p>\n<p>\u63a8\u5bfc\uff1a<\/p>\n<p>\u7531 $x=\\frac{1}{2} at^2$ \u53ef\u5f97\uff1a<\/p>\n<p>$$t_1 = \\sqrt[]{\\frac{2x}{a} } $$<\/p>\n<p>$$t_2=t_1+t_2-t_1=\\sqrt[]{\\frac{4x}{a} } -\\sqrt[]{\\frac{2x}{a} } =\\sqrt[]{\\frac{2x}{a} } \\cdot (\\sqrt[]{2}-1 )$$<\/p>\n<p>$$t_3 = \\sqrt[]{\\frac{6x}{a} } -\\sqrt[]{\\frac{4x}{a} } =\\sqrt[]{\\frac{2x}{a} } \\cdot (\\sqrt[]{3}-\\sqrt[]{2}  )$$<\/p>\n<p>$$\\cdots$$<\/p>\n<p>$t_n=\\sqrt[]{\\frac{2x}{a} } (\\sqrt[]{n}-\\sqrt[]{n-1}  )$$$<\/p>\n<p>\u6545\uff1a<\/p>\n<p>$$t_1:t_2:\\cdots:t_n = 1:(\\sqrt[]{2} -1):(\\sqrt[]{3}-\\sqrt[]{2}  ):\\cdots :(\\sqrt[]{n}-\\sqrt[]{n-1}  )$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u901f\u67e5 $$V_t=V_0+at$$ $$x=V_0t+\\frac{1}{2} at^2$$ $$\\overli [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[24],"_links":{"self":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/459"}],"collection":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/comments?post=459"}],"version-history":[{"count":21,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/459\/revisions"}],"predecessor-version":[{"id":591,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/459\/revisions\/591"}],"wp:attachment":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/media?parent=459"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/categories?post=459"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/tags?post=459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}