{"id":10472,"date":"2022-03-09T15:52:46","date_gmt":"2022-03-09T15:52:46","guid":{"rendered":"https:\/\/10minuteschool.com\/content\/?p=10472"},"modified":"2022-09-04T15:38:53","modified_gmt":"2022-09-04T09:38:53","slug":"deduction-of-equations-of-motion","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/deduction-of-equations-of-motion\/","title":{"rendered":"\u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 (Deduction of Equations of Motion)"},"content":{"rendered":"

\u0985\u09a8\u09cd\u09a4\u09b0\u09c0\u0995\u09b0\u09a3 \u0993 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3<\/a>-\u098f\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 <\/b>(Deduction of Equations of Motion with the help of Differentiation and Integration)<\/b><\/h2>\n

(\u0995) \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 (<\/b>s=vt\u00a0<\/span> \u09ac\u09be <\/b>x=<\/span>x<\/span>0<\/span>+<\/span>v<\/span>x<\/span>t<\/span>)<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964<\/span><\/p>\n

\u09a7\u09b0\u09bf, \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u09b8\u09ae\u09ac\u09c7\u0997<\/span>\u00a0<\/span>=<\/span>\u00a0v<\/span><\/p>\n

\u0986\u09a6\u09bf \u09b8\u09b0\u09a3 <\/span>\u00a0<\/span>=<\/span>\u00a0<\/span>0<\/span><\/p>\n

t<\/span> \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>=<\/span>\u00a0s<\/span><\/p>\n

\u0985\u09a4\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09ae\u09af\u09bc <\/span>dt<\/span> \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>ds<\/span> \u09b9\u09b2\u09c7<\/span><\/p>\n

t+dt\u00a0<\/span>\u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>=s+ds<\/span><\/p>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/span><\/p>\n

\u09ac\u09c7\u0997, <\/span>v=<\/span>ds<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>ds=vdt<\/span> \u2026\u2026\u2026\u2026<\/span> (3.1)<\/span><\/p>\n

\u09af\u0996\u09a8 <\/span>t=0<\/span>, \u09a4\u0996\u09a8 <\/span>s=0<\/span> \u098f\u09ac\u0982 <\/span>t<\/span>=<\/span>t<\/span> \u09a4\u0996\u09a8 <\/span>s=s<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(3.1)<\/span>– \u0995\u09c7 \u0989\u09b2\u09cd\u09b2\u09bf\u0996\u09bf\u09a4 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc,<\/span><\/p>\n

0<\/span>s<\/span>\u200ads=<\/span>0<\/span>t<\/span>\u200avdt<\/span><\/p>\n

\u09ac\u09be, <\/span>0<\/span>s<\/span>\u200ads=v<\/span>0<\/span>t<\/span>\u200adt<\/span>\u00a0 <\/span>[\u2235v\u00a0 <\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span>]<\/span><\/p>\n

\u09ac\u09be, <\/span>s=v\u00d7t<\/span><\/p>\n

\u09af\u09a6\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf <\/span>X-<\/span>\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u0997\u09a4\u09bf\u09b0 \u09b6\u09c1\u09b0\u09c1\u09a4\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09af\u0996\u09a8 <\/span>t\u00a0=\u00a00<\/span>, \u09a4\u0996\u09a8 <\/span>s\u00a0=<\/span>x<\/span>0<\/span> \u098f\u09ac\u0982 \u09af\u0996\u09a8 <\/span>t=t\u00a0<\/span>\u09a4\u0996\u09a8 <\/span>s=x<\/span> \u098f\u09ac\u0982 \u09ac\u09c7\u0997 <\/span>v=<\/span>v<\/span>x<\/span> \u09b9\u09af\u09bc [\u099a\u09bf\u09a4\u09cd\u09b0], \u09a4\u09ac\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(3.1)<\/span>-\u0995\u09c7 \u0989\u09aa\u09b0\u09cb\u0995\u09cd\u09a4 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

x<\/span>0<\/span>x<\/span>\u200ads=<\/span>v<\/span>x<\/span>0<\/span>t<\/span>\u200adt<\/span><\/p>\n

\u09ac\u09be, <\/span>x-<\/span>x<\/span>0<\/span>=<\/span>v<\/span>x<\/span>t<\/span><\/p>\n

\u09ac\u09be, <\/span>[s<\/span>]<\/span>x<\/span>0<\/span>x<\/span>=<\/span>v<\/span>x<\/span>[t<\/span>]<\/span>0<\/span>t<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0 \"Deduction<\/span><\/p>\n

(\u0996) \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b6\u09c7\u09b7 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8<\/b>(<\/span>v=<\/span>v<\/span>0<\/span>+at\u00a0\u00a0<\/span>\u09ac\u09be,<\/b>\u00a0<\/span>v<\/span>x<\/span>=<\/span>v<\/span>x0<\/span>+<\/span>a<\/span>x<\/span>t<\/span>)<\/span><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u0995\u09cb\u09a8 \u098f\u0995\u099f\u09bf \u09a6\u09bf\u0995\u09c7 <\/span>v<\/span>0<\/span> \u0986\u09a6\u09bf \u09ac\u09c7\u0997\u09b8\u09b9 <\/span>a<\/span> \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 \u0985\u09a4\u09bf \u0985\u09b2\u09cd\u09aa <\/span>dt<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 <\/span>v<\/span> \u09b9\u09af\u09bc\u09c7 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09af\u09bc\u09c7 <\/span>v+dv<\/span> \u09b9\u09af\u09bc [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u09a4\u09be\u09b9\u09b2\u09c7,<\/span><\/p>\n

x=<\/span>x<\/span>0<\/span>+<\/span>v<\/span>x<\/span>t<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 \"Deduction<\/span><\/p>\n

\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>a=<\/span>dv<\/span>dt<\/span><\/p>\n

\u09ac\u09be,<\/span> dv\u00a0=adt<\/span>(3.2)<\/span><\/p>\n

\u09af\u0996\u09a8, <\/span>t\u00a0=0\u00a0<\/span>\u09a4\u0996\u09a8 <\/span>v\u00a0=<\/span>v<\/span>0<\/span>\u00a0<\/span>\u098f\u09ac\u0982 \u09af\u0996\u09a8 <\/span>t\u00a0=t\u00a0<\/span> \u09a4\u0996\u09a8 <\/span>v\u00a0=v\u00a0<\/span>\u0964 \u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(3.2)<\/span>-\u098f\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\u09ac\u09be, <\/span> v<\/span>0<\/span>v<\/span>dv=<\/span>0<\/span>t<\/span>adt<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>0<\/span>v<\/span>dv=a<\/span>0<\/span>t<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>v<\/span>0<\/span>v<\/span>=a<\/span>t<\/span>0<\/span>t<\/span><\/p>\n

\u09ac\u09be, <\/span>v\u00a0–<\/span>v<\/span>0<\/span>=at<\/span><\/p>\n

\u09ac\u09be, <\/span>v\u00a0=<\/span>v<\/span>0<\/span>+at<\/span><\/p>\n

\u00a0\u09ac\u09b8\u09cd\u09a4\u09c1 \u09b8\u09ae \u09ae\u09a8\u09cd\u09a6\u09a8\u09c7 \u099a\u09b2\u09b2\u09c7, \u09ae\u09a8\u09cd\u09a6\u09a8 <\/span>= –<\/span>\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>= -a<\/span> \u098f\u09ac\u0982 \u09b8\u09c7\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7,<\/span><\/p>\n

v\u00a0=<\/span>v<\/span>0<\/span>-at<\/span><\/p>\n

(\u0997) \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8<\/b>(s\u00a0=<\/span>v<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>at<\/span>2<\/span> \u09ac\u09be <\/b>x\u00a0=<\/span>x<\/span>0<\/span>+<\/span>v<\/span>x<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>\u00a0<\/span>a<\/span>x<\/span>\u00a0t<\/span>2<\/span>)<\/span><\/h3>\n

\u00a0\u00a0\u00a0\u00a0 \"Deduction<\/span><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be <\/span>v<\/span>0<\/span> \u0986\u09a6\u09bf \u09ac\u09c7\u0997\u09b8\u09b9 \u098f \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964<\/span><\/p>\n

\u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u099f\u09bf <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 <\/span>s<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 <\/span>v<\/span> \u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u098f\u0995\u0987 \u09a6\u09bf\u0995\u09c7 \u0986\u09b0\u09cb \u0985\u09a4\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 <\/span>dt\u00a0<\/span>\u09aa\u09b0\u09c7 <\/span>ds<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u09aa\u09b0 <\/span>v\u00a0=v+dv\u00a0<\/span>\u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09b9\u09af\u09bc [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964<\/span><\/p>\n

\u098f\u0996\u09a8, \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n

a=<\/span>dv<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>dv\u00a0=adt\u2026\u00a0<\/span>(3.3)<\/span><\/p>\n

\u09af\u0996\u09a8, <\/span>t\u00a0=0\u00a0<\/span>\u09a4\u0996\u09a8 <\/span>v\u00a0=<\/span>v<\/span>0<\/span>\u00a0<\/span>\u098f\u09ac\u0982 \u09af\u0996\u09a8 <\/span>t\u00a0=t\u00a0<\/span>\u09a4\u0996\u09a8 <\/span>v\u00a0=v\u00a0;<\/span> \u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(3.3)<\/span>-\u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

v<\/span>0<\/span>v<\/span>dv=<\/span>0<\/span>t<\/span>adt<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>v<\/span>0<\/span>v<\/span>=a<\/span>t<\/span>0<\/span>t<\/span><\/p>\n

\u09ac\u09be, <\/span>v\u00a0–<\/span>v<\/span>0<\/span>=a(t-0)<\/span><\/p>\n

\u09ac\u09be, <\/span>v\u00a0=<\/span>v<\/span>0<\/span>+at <\/span>(3.4)<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

\u09ac\u09be, <\/span>v=<\/span>ds<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>ds\u00a0=vdt<\/span><\/p>\n

\u09ac\u09be, <\/span>ds\u00a0=(<\/span>v<\/span>0<\/span>+at)dt<\/span>\u00a0 [<\/span>(3.4) <\/span>\u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7]<\/span><\/p>\n

\u09ac\u09be, <\/span>ds\u00a0=<\/span>v<\/span>0<\/span>dt+atdt <\/span>(3.5)<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, \u09af\u0996\u09a8, <\/span>t=0\u00a0<\/span>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0997\u09a3\u09a8\u09be\u09b0 \u09b6\u09c1\u09b0\u09c1\u09a4\u09c7\u00a0 <\/span>s\u00a0=0\u00a0<\/span>\u098f\u09ac\u0982 <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09b0\u09c7 <\/span>s\u00a0=s\u00a0\u00a0;\u00a0<\/span>\u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 <\/span>(3.5)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

0<\/span>s<\/span>ds=<\/span>v<\/span>t<\/span>v<\/span>0<\/span>dt+<\/span>v<\/span>t<\/span>atdt<\/span><\/p>\n

\u09ac\u09be, <\/span>0<\/span>s<\/span>ds=<\/span>v<\/span>0<\/span>v<\/span>t<\/span>dt+a<\/span>v<\/span>t<\/span>tdt<\/span><\/p>\n

\u09ac\u09be, <\/span>s<\/span>0<\/span>s<\/span>=<\/span>v<\/span>0<\/span>t<\/span>0<\/span>t<\/span>+a<\/span>t<\/span>2<\/span>2<\/span>0<\/span>t<\/span><\/p>\n

\u09ac\u09be, <\/span>s-0<\/span>=<\/span>v<\/span>0<\/span>t-0<\/span>+a\u00a0<\/span>t<\/span>2<\/span>2<\/span>–<\/span>0<\/span>2<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>s\u00a0=<\/span>v<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>at<\/span>2<\/span>(3.6)<\/span><\/p>\n

\"Deduction<\/p>\n

\u0986\u09ac\u09be\u09b0, \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b9\u09a4\u09c7 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b9\u09b2\u09c7, \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n

s\u00a0=0\u00d7t+<\/span>1<\/span>2<\/span>at<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>s\u00a0=0+<\/span>1<\/span>2<\/span>at<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>s\u00a0=<\/span>1<\/span>2<\/span>at<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>s\u00a0=<\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span>\u00a0\u00d7\u00a0<\/span>t<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>s\u00a0\u221d\u00a0<\/span>t<\/span>2<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b9\u09a4\u09c7 \u09b8\u09ae-\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/span><\/p>\n

\u099a\u09bf\u09a4\u09cd\u09b0 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09df\u09c7\u099b\u09c7\u0964<\/span><\/p>\n

\u09af\u09a6\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf <\/span>X<\/span> \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b9\u09af\u09bc \u098f\u09ac\u0982 <\/span>t=0<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u0986\u09a6\u09bf\u09ac\u09c7\u0997 <\/span>=<\/span> v<\/span>x<\/span>0<\/span>, \u0985\u09a8\u09cd\u09af \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09af\u09bc <\/span>t<\/span>-\u09a4\u09c7 \u09b6\u09c7\u09b7 \u09ac\u09c7\u0997 <\/span>=<\/span> v<\/span> \u0993 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>a<\/span>x<\/span> \u09a7\u09b0\u09be \u09b9\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(3.6)<\/span>\u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc,\u00a0<\/span><\/p>\n

s\u00a0=<\/span>v<\/span>x<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>a<\/span>x<\/span>t<\/span>2<\/span><\/p>\n

\u098f\u0996\u09a8 <\/span>s\u00a0=0\u00a0<\/span>\u09b8\u09ae\u09af\u09bc\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>x<\/span>0<\/span>\u098f\u09ac\u0982 <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u098f\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>x<\/span> \u09b9\u09b2\u09c7, <\/span>s=x-<\/span>x<\/span>0<\/span>\u00a0<\/span>\u09b9\u09ac\u09c7\u0964 \u09b8\u09c7\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7<\/span><\/p>\n

s=x-<\/span>x<\/span>0<\/span>=<\/span>v<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>a<\/span>x<\/span>t<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>x=<\/span>x<\/span>0<\/span>–<\/span>v<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>a<\/span>x<\/span>t<\/span>2<\/span> (3.7)<\/span><\/p>\n

\u09ac\u09b8\u09cd\u09a4\u09c1 <\/span>a<\/span> \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u09a8\u09be \u099a\u09b2\u09c7 <\/span>a\u00a0<\/span> \u09b8\u09ae\u09ae\u09a8\u09cd\u09a6\u09a8\u09c7 \u099a\u09b2\u09b2\u09c7, \u09ae\u09a8\u09cd\u09a6\u09a8 <\/span>= – <\/span>\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>= – a\u00a0<\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(3.7)<\/span>\u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

s\u00a0=<\/span>v<\/span>0<\/span>t-<\/span>1<\/span>2<\/span>at<\/span>2<\/span><\/p>\n

\u00a0\u00a0\u00a0 \"Deduction<\/span><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 <\/span>a<\/span>x<\/span> \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u098f\u09ac\u0982 \u0997\u09a3\u09a8\u09be\u09b0 \u09b6\u09c1\u09b0\u09c1\u09a4\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09af\u0996\u09a8 <\/span>t=0\u00a0<\/span><\/p>\n

\u09a4\u0996\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>=<\/span> x<\/span>0<\/span>. \u09ac\u09c7\u0997 <\/span>=<\/span> v<\/span>x<\/span>0<\/span>, \u098f\u09ac\u0982 <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>= x<\/span>, \u09ac\u09c7\u0997 <\/span>=<\/span> v<\/span>x<\/span>; \u098f\u0996\u09a8, \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u098f\u0995\u0987 \u09a6\u09bf\u0995\u09c7 \u0986\u09b0\u0993 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09ae\u09af\u09bc <\/span>dt<\/span> \u09aa\u09b0\u09c7, <\/span>dx<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 <\/span>v<\/span>x<\/span>+d<\/span>v<\/span>x<\/span> \u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b9\u09b2\u09c7, \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

a<\/span>x<\/span>=<\/span>d<\/span>v<\/span>x<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>d<\/span>v<\/span>x<\/span>\u00a0=<\/span>a<\/span>x<\/span>dt\u00a0\u2026\u2026\u2026<\/span>\u00a0<\/span><\/i>(3.8)<\/span><\/p>\n

\u099a\u09bf\u09a4\u09cd\u09b0 <\/span>(3.8)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09af\u09a5\u09be\u09af\u09a5 \u09b8\u09c0\u09ae\u09be \u09a4\u09a5\u09be <\/span>t = 0<\/span> \u0993\u00a0 <\/span>t=t<\/span> \u098f\u09ac\u0982 <\/span>v<\/span>x<\/span>0<\/span> \u0993 <\/span>v<\/span>x<\/span>\u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

v<\/span>x<\/span>0<\/span>v<\/span>x<\/span>d<\/span>v<\/span>x<\/span>=<\/span>0<\/span>t<\/span>a<\/span>x<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>v<\/span>x<\/span>0<\/span>v<\/span>x<\/span>=<\/span>a<\/span>x<\/span>t<\/span>0<\/span>t<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>x<\/span>–<\/span>v<\/span>x<\/span>0<\/span>=<\/span>a<\/span>x<\/span>(t-0)<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>x<\/span>=<\/span>v<\/span>x<\/span>0<\/span>+<\/span>a<\/span>x<\/span>t <\/span>(3.9)<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

v<\/span>x<\/span>=<\/span>dx<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>dx\u00a0=<\/span>v<\/span>x<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>dx\u00a0=(<\/span>v<\/span>x<\/span>0<\/span>+<\/span>a<\/span>x<\/span>t)dt <\/span>(3.10)<\/span> [<\/span>(3.9)<\/span> \u09a8\u0982<\/span>\u00a0<\/span>\u098f\u09b0<\/span>\u00a0<\/span>\u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7<\/span>]<\/span><\/p>\n

(3.10)<\/span> \u09a8\u0982 \u098f\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 <\/span>x<\/span>0<\/span> \u0993 <\/span>x<\/span> \u098f\u09ac\u0982 <\/span>t=0\u00a0<\/span>\u0993 <\/span>t\u00a0<\/span>\u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

x<\/span>0<\/span>x<\/span>d<\/span>v<\/span>x<\/span>=<\/span>0<\/span>t<\/span>(v<\/span>x<\/span>0<\/span>+<\/span>a<\/span>x<\/span>t)dt<\/span>\u00a0<\/span><\/p>\n

\u09ac\u09be, <\/span>x<\/span>x<\/span>0<\/span>x<\/span>=<\/span>v<\/span>0<\/span>t<\/span>0<\/span>t<\/span>+<\/span>a<\/span>x<\/span>t<\/span>2<\/span>2<\/span>0<\/span>t<\/span><\/p>\n

\u09ac\u09be, <\/span>x-<\/span>x<\/span>0<\/span>\u00a0=<\/span>v<\/span>x<\/span>0<\/span>t+<\/span>a<\/span>x<\/span>1<\/span>2<\/span>t<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>x=<\/span>x<\/span>0<\/span>–<\/span>v<\/span>x<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>a<\/span>x<\/span>at<\/span>2<\/span><\/h3>\n

(\u0998) \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0986\u09a6\u09bf \u09ac\u09c7\u0997, \u09b6\u09c7\u09b7 \u09ac\u09c7\u0997 \u098f\u09ac\u0982 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (<\/b>v<\/span>2<\/span>=<\/span>v<\/span>0<\/span>2<\/span>+2as\u00a0<\/span>\u09ac\u09be<\/b>\u00a0<\/b>v<\/span>x<\/span>2<\/span>=<\/span>v<\/span>x<\/span>0<\/span>2<\/span>+\u00a0 \u00a0 \u00a0 \u00a0 2a(x-<\/span>x<\/span>0<\/span>)<\/span>:<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 <\/span>a<\/span> \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0986\u09a6\u09bf \u09ac\u09c7\u0997 =<\/span>v<\/span>0<\/span>; <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09b0\u09c7 \u09a4\u09be\u09b0 \u09b6\u09c7\u09b7 \u09ac\u09c7\u0997 <\/span>=<\/span> v<\/span> \u098f\u09ac\u0982 \u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09af\u09bc\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf <\/span>s<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7\u0964 <\/span>v<\/span>,<\/span> \u00a0v<\/span>0<\/span>, <\/span>a<\/span> \u0993 <\/span>s<\/span>-\u098f\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u099c\u09a8\u09bf\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

a=<\/span>dv<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>a=<\/span>dv<\/span>ds<\/span>\u00d7<\/span>ds<\/span>ds<\/span><\/p>\n

\u09ac\u09be, <\/span>a=<\/span>dv<\/span>ds<\/span>\u00d7v<\/span><\/p>\n

\u09ac\u09be, <\/span>ads=v\u00d7dv <\/span>(3.11)<\/span><\/p>\n

\u09af\u0996\u09a8, <\/span>s=0\u00a0\u00a0<\/span>\u09a4\u0996\u09a8 <\/span>\u00a0v=<\/span>v<\/span>0<\/span>\u00a0<\/span>\u098f\u09ac\u0982 \u09af\u0996\u09a8 <\/span>s\u00a0=s<\/span> \u09a4\u0996\u09a8 <\/span>v=v\u00a0\u00a0;\u00a0<\/span>\u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 <\/span>(3.11)\u00a0<\/span>\u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

0<\/span>s<\/span>ads=<\/span>v<\/span>0<\/span>v<\/span>vdv<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>0<\/span>s<\/span>ds=<\/span>v<\/span>0<\/span>v<\/span>vdv<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>s<\/span>0<\/span>s<\/span>=<\/span>v<\/span>2<\/span>2<\/span>v<\/span>0<\/span>v<\/span><\/p>\n

\u09ac\u09be, <\/span>a(s-0)\u00a0=<\/span>v<\/span>2<\/span>2<\/span>–<\/span>v<\/span>0<\/span>2<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>as\u00a0=<\/span>v<\/span>2<\/span>–<\/span>v<\/span>0<\/span>2<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>2as\u00a0=<\/span>v<\/span>2<\/span>–<\/span>v<\/span>0<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>2<\/span>=<\/span>v<\/span>0<\/span>2<\/span>+2as<\/span><\/p>\n

\u0986\u09ac\u09be\u09b0, \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b9\u09a4\u09c7 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u099a\u09b2\u09be \u09b6\u09c1\u09b0\u09c1 \u0995\u09b0\u09b2\u09c7, \u0986\u09ae\u09be\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>2<\/span>=<\/span>0<\/span>2<\/span>+2as<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>2<\/span>=2as<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>2<\/span>=<\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span>\u00a0\u00d7s<\/span> [<\/span>\u2235<\/span> 2a\u00a0<\/span> \u09a7\u09cd\u09b0\u09c1\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be ]<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>2<\/span>\u221ds<\/span><\/p>\n

\u09ac\u09be, <\/span>v\u221d<\/span>s<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09b9\u09a4\u09c7 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b6\u09c7\u09b7 \u09ac\u09c7\u0997 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09ae\u09c2\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964\u00a0\u00a0<\/span><\/p>\n

v<\/span>x<\/span>2<\/span>=<\/span>v<\/span>x<\/span>0<\/span>2<\/span>+2a(x-<\/span>x<\/span>0<\/span>)<\/span> [ \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 ]<\/span><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 <\/span>X<\/span>– \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 <\/span>a<\/span>x<\/span> \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0964<\/span><\/p>\n

\u0997\u09a3\u09a8\u09be\u09b0 \u09b6\u09c1\u09b0\u09c1\u09a4\u09c7, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09af\u0996\u09a8 \u09b8\u09ae\u09df <\/span>t=0<\/span>; \u09a4\u0996\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0986\u09a6\u09bf\u09ac\u09c7\u0997 <\/span>v<\/span>x<\/span>0<\/span> \u098f\u09ac\u0982 \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 =<\/span>\u00a0<\/span>x<\/span>0<\/span> \u098f\u09ac\u0982 <\/span>t\u00a0<\/span>\u09b8\u09ae\u09af\u09bc\u09c7 \u09aa\u09b0 \u09ac\u09c7\u0997<\/span> =<\/span> v<\/span>x<\/span> \u098f\u09ac\u0982 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>=x<\/span><\/p>\n

\"Deduction<\/p>\n

\u098f\u0996\u09a8 \u0990 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0\u0987 \u0986\u09b0\u09cb \u0985\u09a4\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09ae\u09df <\/span>dt<\/span> \u09aa\u09b0\u09c7 <\/span>v<\/span>x<\/span>+d<\/span>v<\/span>x<\/span> \u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b9\u09b2\u09c7, \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n

a<\/span>x<\/span>=<\/span>d<\/span>v<\/span>x<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>=<\/span>d<\/span>v<\/span>x<\/span>dx<\/span>\u00d7<\/span>dx<\/span>dt<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>=<\/span>d<\/span>v<\/span>x<\/span>dx<\/span>v<\/span>x<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>dx=<\/span>v<\/span>x<\/span>dv<\/span>x<\/span> \u00a0<\/span>(3.12)<\/span><\/p>\n

\u09af\u0996\u09a8,<\/span>\u00a0\u00a0x=<\/span>x<\/span>0<\/span>\u09a4\u0996\u09a8 <\/span>\u00a0v=<\/span>v<\/span>x<\/span>0<\/span>\u00a0<\/span>\u098f\u09ac\u0982 \u09af\u0996\u09a8 <\/span>x\u00a0=x<\/span> \u09a4\u0996\u09a8 <\/span>v=<\/span>v<\/span>x<\/span>\u00a0\u00a0;\u00a0<\/span>\u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 <\/span>(3.12)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

x<\/span>0<\/span>x<\/span>a<\/span>x<\/span>dx=<\/span>v<\/span>x<\/span>0<\/span>v<\/span>x<\/span>v<\/span>x<\/span>dx<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>x<\/span>0<\/span>x<\/span>dx=<\/span>v<\/span>x<\/span>0<\/span>v<\/span>x<\/span>v<\/span>x<\/span>dx<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>x<\/span>x<\/span>0<\/span>x<\/span>=<\/span>v<\/span>x<\/span>2<\/span>2<\/span>v<\/span>x<\/span>0<\/span>v<\/span>x<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>(x-<\/span>x<\/span>0<\/span>)\u00a0=<\/span>v<\/span>x<\/span>2<\/span>2<\/span>–<\/span>v<\/span>x<\/span>0<\/span>2<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>a<\/span>x<\/span>(x-<\/span>x<\/span>0<\/span>)=<\/span>v<\/span>x<\/span>2<\/span>–<\/span>v<\/span>x<\/span>0<\/span>2<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>x<\/span>2<\/span>–<\/span>v<\/span>x<\/span>0<\/span>2<\/span>=2a<\/span>x<\/span>(x-<\/span>x<\/span>0<\/span>)<\/span><\/p>\n

\u09ac\u09be, <\/span>v<\/span>x<\/span>2<\/span>=<\/span>v<\/span>x<\/span>0<\/span>2<\/span>+2a<\/span>x<\/span>(x-<\/span>x<\/span>0<\/span>)<\/span><\/p>\n

\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 <\/b>(Deduction of Equations of Motion from Graphs)<\/b><\/h2>\n

(\u0995) <\/b>s\u00a0=<\/span>v<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>at<\/span>2<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 \"Deduction<\/span><\/p>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u098f\u09b0 \u09ac\u09c7\u0997 <\/span>v<\/span> \u098f\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09b2\u09cb: <\/span>v\u00a0=<\/span>v<\/span>0<\/span>+at<\/span><\/p>\n

\u098f\u0996\u09a8 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09b8\u09ae\u09af\u09bc <\/span>t<\/span> \u098f\u09ac\u0982 <\/span>Y<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09ac\u09c7\u0997 <\/span>v<\/span> \u09a8\u09bf\u09af\u09bc\u09c7 <\/span>v<\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span> \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964 (\u099a\u09bf\u09a4\u09cd\u09b0)\u0964\u00a0<\/span><\/p>\n

\u098f\u099f\u09bf <\/span>Y<\/span>-\u0985\u0995\u09cd\u09b7\u0995\u09c7 \u099b\u09c7\u09a6\u0995\u09be\u09b0\u09c0 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b9\u09af\u09bc \u09af\u09be <\/span>\u00a0y=mx+c\u00a0 <\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, <\/span>v<\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span> \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a5\u09c7\u0995\u09c7 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09b2\u09c7 \u09af\u09c7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u09b9\u09af\u09bc \u09a4\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7 <\/span>v<\/span> \u098f\u09ac\u0982 <\/span>t<\/span> \u098f\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2 \u09a4\u09a5\u09be \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>s\u00a0<\/span>\u0964<\/span><\/p>\n

AB<\/span> \u09b0\u09c7\u0996\u09be\u09b0 \u0989\u09aa\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>P<\/span> \u09a8\u09c7\u09af\u09bc\u09be \u09b9\u09af\u09bc\u0964 <\/span>P<\/span> \u09a5\u09c7\u0995\u09c7 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0989\u09aa\u09b0 <\/span>PQ<\/span> \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09be \u09b9\u09af\u09bc\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>OP<\/span> =<\/span> t<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>s<\/span> \u09b9\u09ac\u09c7\u0964 <\/span>AOQP<\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u0964<\/span><\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>a<\/span> \u098f\u09ac\u0982 \u0986\u09a6\u09bf\u09f0\u09c7\u0997, <\/span>v<\/span>0<\/span>= OA<\/span><\/p>\n

\u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09b8\u09ae\u09af\u09bc, <\/span>t=<\/span> OQ<\/span><\/p>\n

\u098f\u09ac\u0982 <\/span>t\u00a0<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac, <\/span>s<\/span> = AOQP <\/span>\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>= AOQR<\/span> \u0986\u09af\u09bc\u09a4\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 <\/span>+ ARP<\/span> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u0964<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>= AO \u00d7 OQ + <\/span>1<\/span>2<\/span> \u00d7AR \u00d7 PR<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u09ac\u09be, <\/span>s = AO \u00d7 OQ + <\/span>1<\/span>2<\/span> \u00d7 OQ \u00d7 PR [\u2235AR=OQ]<\/span><\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 <\/span>AB<\/span> \u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 \u09b9\u099a\u09cd\u099b\u09c7 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>a<\/span>,<\/span><\/p>\n

\u2234<\/span>\u00a0a=\u00a0<\/span>PR<\/span>AR<\/span><\/p>\n

\u2234<\/span>\u00a0PR=a\u00d7AR<\/span><\/p>\n

=a\u00d7<\/span> OQ<\/span><\/p>\n

\u2234s<\/span> = AO \u00d7 OQ +<\/span> 1<\/span>2<\/span> a\u00a0\u00d7<\/span>OQ<\/span>2<\/span><\/p>\n

\u09ac\u09be, <\/span>s\u00a0=<\/span>v<\/span>0<\/span>t+<\/span>1<\/span>2<\/span>at<\/span>2<\/span><\/p>\n

(\u0996) <\/b>v<\/span>2<\/span>=<\/span>v<\/span>0<\/span>2<\/span>+2as -\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09ac\u09c7\u0997 <\/span>v\u00a0<\/span>-\u098f\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09b2\u09cb <\/span>v\u00a0=<\/span>v<\/span>0<\/span>+at<\/span>\u0964 \u098f\u0996\u09a8 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09b8\u09ae\u09af\u09bc <\/span>t<\/span> \u098f\u09ac\u0982 <\/span>Y<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09ac\u09c7\u0997 <\/span>v<\/span> \u09a8\u09bf\u09af\u09bc\u09c7 <\/span>v<\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span> \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u0985\u0999\u09cd\u0995\u09a8 \u0995\u09b0\u09be \u09b9\u09af\u09bc (\u099a\u09bf\u09a4\u09cd\u09b0)\u0964 \u098f\u099f\u09bf <\/span>Y<\/span> \u0985\u0995\u09cd\u09b7\u0995\u09c7 \u099b\u09c7\u09a6\u0995\u09be\u09b0\u09c0 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b9\u09af\u09bc \u09af\u09be <\/span>y=mx+c\u00a0 <\/span>\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09ae\u09c7\u09a8\u09c7 \u099a\u09b2\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, <\/span>v<\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span> \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u09c7\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a5\u09c7\u0995\u09c7 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09b2\u09c7 \u09af\u09c7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 \u0989\u09ce\u09aa\u09a8\u09cd\u09a8 \u09b9\u09af\u09bc \u09a4\u09be\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 <\/span>v<\/span> \u098f\u09ac\u0982 <\/span>t<\/span> \u098f\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2 \u09a4\u09a5\u09be \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>s\u00a0<\/span> \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964\u00a0<\/span><\/p>\n

AB<\/span> \u09b0\u09c7\u0996\u09be\u09b0 \u0989\u09aa\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 <\/span>P<\/span> \u09a8\u09c7\u09af\u09bc\u09be \u09b9\u09af\u09bc\u0964 <\/span>P<\/span> \u09a5\u09c7\u0995\u09c7 <\/span>X<\/span>-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0989\u09aa\u09b0 <\/span>PQ<\/span> \u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09be \u09b9\u09af\u09bc\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 <\/span>OQ = t<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>s\u00a0<\/span> \u09b9\u09ac\u09c7 <\/span>AOQP<\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u0964<\/span><\/p>\n

\u098f\u09ac\u0982 \u0986\u09a6\u09bf\u09ac\u09c7\u0997, <\/span>v<\/span>0<\/span> = OA<\/span><\/p>\n

\u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09b8\u09ae\u09af\u09bc, <\/span>t\u00a0= OQ<\/span><\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3<\/span> =<\/span> a<\/span><\/p>\n

\u22342s\u00a0=OQ (2OA\u00a0 + RP)<\/span><\/p>\n

=OQ (OA + OA\u00a0 + RP)<\/span><\/p>\n

\u098f\u09ac\u0982 <\/span>t<\/span> \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>s=<\/span> AOQP<\/span> \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>=\u00a0AOQR<\/span> \u0986\u09af\u09bc\u09a4\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2<\/span> + ARP<\/span> \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>=OQ \u00d7 OA+<\/span> OQ\u00d7RP<\/span>2<\/span><\/p>\n

\u2234<\/span> s\u00a0<\/span> =OQ \u00d7 OA+<\/span> 1<\/span>2<\/span>\u00d7AR\u00d7RP<\/span><\/p>\n

\u2234<\/span>\u00a0a=\u00a0<\/span>RP<\/span>AR<\/span><\/p>\n

2s=<\/span>v<\/span>2<\/span>–<\/span>v<\/span>0<\/span>2<\/span>a<\/span><\/p>\n

\u2234v<\/span>2<\/span>–<\/span>v<\/span>0<\/span>2<\/span>=<\/span> 2as<\/span><\/p>\n

v<\/span>2<\/span>=<\/span>v<\/span>0<\/span>2<\/span>+<\/span> 2as<\/span><\/p>\n

2s=<\/span>(v-<\/span>v<\/span>0<\/span>)(v+<\/span>v<\/span>0<\/span>)<\/span>a<\/span><\/p>\n

2s=<\/span>QP-QR<\/span>\u00a0<\/span>a<\/span> (v+<\/span>v<\/span>0<\/span>)<\/span><\/p>\n

\u22342s=<\/span>RP\u00a0<\/span>a<\/span> (v+<\/span>v<\/span>0<\/span>)<\/span> \u00a0 <\/span>[\u2235OA=<\/span>v<\/span>0<\/span> \u098f\u09ac\u0982 <\/span>\u00a0<\/span>QP=v<\/span>]<\/span><\/p>\n

\u2234<\/span>AR=\u00a0<\/span>RP<\/span>a<\/span><\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 <\/span>AB<\/span> \u098f\u09b0 \u09a2\u09be\u09b2 \u09b9\u099a\u09cd\u099b\u09c7 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>a<\/span><\/p>\n

=AR (OA + QR + RP)<\/span><\/p>\n

=AR (OA + QP)<\/span><\/p>\n

=OQ<\/span>2OA+RP<\/span>2<\/span><\/p>\n

=OQ<\/span>OA+<\/span>RP<\/span>2<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0985\u09a8\u09cd\u09a4\u09b0\u09c0\u0995\u09b0\u09a3 \u0993 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3-\u098f\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 (Deduction of Equations of Motion with the help of Differentiation and Integration) (\u0995) \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 (s=vt\u00a0 \u09ac\u09be x=x0+vxt) \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964 \u09a7\u09b0\u09bf, \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u09b8\u09ae\u09ac\u09c7\u0997\u00a0=\u00a0v<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[50,3028,51],"tags":[3839,3838,3840],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/10472"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=10472"}],"version-history":[{"count":5,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/10472\/revisions"}],"predecessor-version":[{"id":15495,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/10472\/revisions\/15495"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=10472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=10472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=10472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}