{"id":3859,"date":"2021-01-30T12:25:51","date_gmt":"2021-01-30T12:25:51","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3859"},"modified":"2022-04-04T03:09:23","modified_gmt":"2022-04-03T21:09:23","slug":"average-velocity","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/average-velocity\/","title":{"rendered":"\u0997\u09a1\u09bc \u09ac\u09c7\u0997 | Average Velocity"},"content":{"rendered":"

\u0997\u09a1\u09bc \u09ac\u09c7\u0997 (Average Velocity)<\/b><\/h2>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 <\/span>u<\/span><\/span> \u0986\u09a6\u09bf\u09ac\u09c7\u0997\u09c7 \u098f\u09ac\u0982 <\/span>f<\/span><\/span> \u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u09af\u09be\u09a4\u09cd\u09b0\u09be \u0995\u09b0\u09c7 <\/span>t<\/span><\/span> \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7 <\/span>s<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 <\/span>v<\/span><\/span> \u09ac\u09c7\u0997 \u0985\u09b0\u09cd\u099c\u09a8 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987, <\/span>v=u+f t<\/span><\/span> \u098f\u09ac\u0982 s=u t+\\frac{1}{2} f t^{2}<\/span><\/span><\/p>\n\\begin{aligned} \\therefore \\text { \u0997\u09dc\u09ac\u09c7\u0997 } &=\\frac{\\text { \u09ae\u09cb\u099f \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac }}{\\text { \u09ae\u09cb\u099f \u09b8\u09ae\u09af\u09bc }}=\\frac{s}{t}=\\frac{u t+\\frac{1}{2} f t^{2}}{t}=u+\\frac{1}{2} f t=\\text { \u09ae\u09a7\u09cd\u09af \u09b8\u09ae\u09df\u09c7 \u09ac\u09c7\u0997 } \\\\ &=\\frac{1}{2}(2 u+f t)=\\frac{1}{2}\\{u+(u+f t)\\}=\\frac{1}{2}(u+v)=\\frac{1}{2} \\text { (\u0986\u09a6\u09bf\u09ac\u09c7\u0997 + \u0985\u09a8\u09cd\u09a4\u0983\u09ac\u09c7\u0997) } \\end{aligned}<\/span>\n

N.B.: s=u t+\\frac{1}{2} f t^{2}=\\frac{2 u t+f t^{2}}{2}=\\frac{u+(u+f t)}{2} \\times t=\\frac{u+v}{2} \\times t<\/span><\/b>\u00a0<\/span><\/p>\n

\\therefore<\/span><\/span> \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u099a\u09b2\u09ae\u09be\u09a8 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac <\/span>=<\/span> \u0997\u09a1\u09bc\u09ac\u09c7\u0997 \\times<\/span> <\/span>\u09b8\u09ae\u09af\u09bc<\/span><\/p>\n

\u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5\u09c7\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 (Graph of the motion of a particle)<\/b><\/h2>\n

\u09b6\u09c2\u09a8\u09cd\u09af \u09a4\u09cd\u09ac\u09b0\u09a3 \u09ac\u09be \u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0:<\/b><\/h3>\n

\u09a4\u09cd\u09ac\u09b0\u09a3 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09b2\u09c7 \u0986\u09a6\u09bf\u09ac\u09c7\u0997 \u0993 \u09b6\u09c7\u09b7 \u09ac\u09c7\u0997 \u09b8\u09ae\u09be\u09a8 \u09b9\u09af\u09bc \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>u = v<\/span><\/span> \u09b9\u09af\u09bc\u0964 \u09a4\u0996\u09a8 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09ac\u09c7\u0997 \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7\u0964 \u0997\u09a4\u09bf\u09b0 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0987 s = v t<\/span> <\/span>\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>s<\/span><\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span><\/span> \u09ac\u09be (s - t)<\/span><\/span>\u00a0\u09b2\u09c7\u0996 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09af\u09be\u09b0 \u09a2\u09be\u09b2 <\/span>v<\/span><\/span><\/p>\n

\"\u09b6\u09c2\u09a8\u09cd\u09af<\/p>\n

\"\u09b6\u09c2\u09a8\u09cd\u09af<\/p>\n

\u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0:<\/b><\/h3>\n

\u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09a7\u09cd\u09b0\u09c1\u09ac \u09a5\u09be\u0995\u09c7\u0964 \u0997\u09a4\u09bf\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u09aa\u09be\u0987, v=u+f t<\/span><\/span>\u00a0\u098f\u09ac\u0982 <\/span>s=u t+<\/span>\\frac{1}{2} f t^{2}<\/span><\/span>\u00a0\u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>v<\/span><\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span><\/span> \u09ac\u09be, <\/span>(v-t)<\/span><\/span> \u09b2\u09c7\u0996 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u098f\u09ac\u0982 <\/span>s<\/span><\/span> \u09ac\u09a8\u09be\u09ae <\/span>t<\/span><\/span> \u09ac\u09be (s-t)<\/span><\/span>\u00a0\u09b2\u09c7\u0996 \u098f\u0995\u099f\u09bf \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u0964<\/span><\/p>\n

\"\u09b8\u09c1\u09b7\u09ae-\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7-\u0997\u09a4\u09bf\u09b6\u09c0\u09b2-\u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0-F-\u09ac\u09a8\u09be\u09ae-T\u09b2\u09c7\u0996\"<\/p>\n

\"\u09b8\u09c1\u09b7\u09ae-\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7-\u0997\u09a4\u09bf\u09b6\u09c0\u09b2-\u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0-U-\u09ac\u09a8\u09be\u09ae-T\u09b2\u09c7\u0996\"<\/p>\n

\"\u09b8\u09c1\u09b7\u09ae-\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7-\u0997\u09a4\u09bf\u09b6\u09c0\u09b2-\u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0-S-\u09ac\u09a8\u09be\u09ae-T\u09b2\u09c7\u0996\"<\/p>\n

\u0985\u09b8\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0:<\/b><\/h3>\n

\u0995\u09cb\u09a8\u09cb \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09a3\u09be \u0986\u09a6\u09bf \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09a5\u09c7\u0995\u09c7 <\/span>f<\/span><\/span> \u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 t_{1}<\/span><\/span> \u09b8\u09ae\u09df\u09c7 s_{1}<\/span><\/span>, \u09b6\u09c2\u09a8\u09cd\u09af\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 t_{2}<\/span><\/span> \u09b8\u09ae\u09df\u09c7 s_{2}<\/span><\/span>\u00a0\u098f\u09ac\u0982 <\/span>f<\/span><\/span> \u09b8\u09c1\u09b7\u09ae \u09ae\u09a8\u09cd\u09a6\u09a8\u09c7 t_{3}<\/span><\/span> \u09b8\u09ae\u09df\u09c7 s_{3}<\/span><\/span>\u00a0\u09aa\u09a5 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u09ac\u09c7\u0997 \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09b2\u09c7\u0996\u00a0\u00a0<\/span><\/p>\n

\"\u0985\u09b8\u09ae<\/p>\n

\"\u0985\u09b8\u09ae<\/p>\n

(i) <\/b>v = u + f t<\/span><\/span> \u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0:\u00a0<\/b><\/h4>\n

\u098f\u0995\u099f\u09bf \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be <\/span>u<\/span><\/span> \u0986\u09a6\u09bf\u09ac\u09c7\u0997\u09c7 \u09af\u09be\u09a4\u09cd\u09b0\u09be \u0995\u09b0\u09c7 <\/span>f<\/span><\/span> \u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 <\/span>t<\/span><\/span> \u09b8\u09ae\u09df \u099a\u09b2\u09c7 <\/span>v<\/span><\/span> \u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b9\u09b2\u09c7,\u00a0<\/span><\/p>\n

v=u+f t \\ldots \\text {...(1) }<\/span><\/span><\/p>\n

u<\/span><\/span> \u0993 <\/span>f<\/span><\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09c7 <\/span>v<\/span><\/span> \u098f\u09b0 \u09ae\u09be\u09a8 <\/span>t<\/span><\/span> \u098f\u09b0 \u09ae\u09be\u09a8\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 <\/span>t<\/span><\/span> \u09b8\u09cd\u09ac\u09be\u09a7\u09c0\u09a8 \u099a\u09b2\u0995 \u098f\u09ac\u0982 <\/span>v<\/span><\/span> \u0985\u09a7\u09c0\u09a8 \u099a\u09b2\u0995\u0964<\/span><\/p>\n

v=y, u=c, f=m<\/span><\/span> \u098f\u09ac\u0982 <\/span>t=x<\/span><\/span> \u09a7\u09b0\u09b2\u09c7 <\/span>(1)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987, <\/span>y=m x+c<\/span> ;<\/span> \u09af\u09be \u0995\u09be\u09b0\u09cd\u09a4\u09c7\u09b8\u09c0\u09df \u09a4\u09b2\u09c7 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 v=u+f t<\/span><\/span>\u00a0\u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

u=0<\/span><\/span> \u09b9\u09b2\u09c7, <\/span>v=f t<\/span><\/span> \u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u0964\u00a0<\/span><\/p>\n

\"\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\"<\/p>\n

\"\u0986\u09a6\u09bf-\u09ac\u09c7\u0997-\u09b6\u09c2\u09a8\u09cd\u09af-\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\"<\/p>\n

(ii) <\/b>s=u t+\\frac{1}{2} f t^{2}<\/span><\/span>\u00a0\u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0:\u00a0<\/b><\/h4>\n

u<\/span><\/span> \u0986\u09a6\u09bf\u09ac\u09c7\u0997\u09c7 \u09af\u09be\u09a4\u09cd\u09b0\u09be \u0995\u09b0\u09c7 <\/span>f<\/span><\/span> \u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u098f\u0995\u099f\u09bf \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be <\/span>t<\/span><\/span> \u09b8\u09ae\u09af\u09bc\u09c7 <\/span>s<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09b2\u09c7,<\/span><\/p>\n

\u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3, s=u t+\\frac{1}{2} f t^{2} \\ldots \\ldots<\/span> (1)<\/span><\/p>\n

u<\/span><\/span> \u0993 <\/span>f<\/span><\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09c7 <\/span>s<\/span>, t<\/span><\/span> \u098f\u09b0 \u098f\u0995\u099f\u09bf \u09ab\u09be\u0982\u09b6\u09a8\u0964 u=a, \\frac{1}{2} f=b, t=x, s=y<\/span><\/span> \u09a7\u09b0\u09b2\u09c7 \u09aa\u09be\u0987 y=a x+b x^{2}<\/span><\/span>; \u09af\u09be \u0995\u09be\u09b0\u09cd\u09a4\u09c7\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 s=u t+\\frac{1}{2} f t^{2}<\/span><\/span>\u00a0\u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u0986\u09a6\u09bf\u09ac\u09c7\u0997 <\/span>(u)<\/span><\/span> \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09b2\u09c7<\/span>\u00a0 s=\\frac{1}{2} f t^{2}<\/span><\/span>\u00a0\u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\"\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0-1\"<\/p>\n

 <\/p>\n

(iii) <\/b>v^{2}=u^{2}+2 f s<\/span><\/span>\u00a0\u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0:\u00a0<\/b><\/h4>\n

u<\/span><\/span> \u0986\u09a6\u09bf\u09ac\u09c7\u0997\u09c7 \u09af\u09be\u09a4\u09cd\u09b0\u09be \u0995\u09b0\u09c7 <\/span>f<\/span><\/span> \u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u098f\u0995\u099f\u09bf \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be <\/span>s<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 <\/span>v<\/span><\/span> \u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09b9\u09b2\u09c7 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3, v^{2}=u^{2}+2 f s<\/span> <\/span>\u0964 <\/span>u<\/span><\/span> \u0993 <\/span>f<\/span><\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09b2\u09c7 <\/span>v, s<\/span><\/span> \u098f\u09b0 \u098f\u0995\u099f\u09bf \u09ab\u09be\u0982\u09b6\u09a8 \u0964<\/span><\/p>\n

u^{2}=a, 2 f=b, s=x<\/span> \u09a7\u09b0\u09b2\u09c7, y^{2}=a+b x^{2}<\/span><\/span>; \u09af\u09be \u0995\u09be\u09b0\u09cd\u09a4\u09c7\u09b8\u09c0\u09af\u09bc \u09a4\u09b2\u09c7 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 v^{2}=u^{2}+2 f s<\/span><\/span>\u00a0\u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09aa\u09b0\u09be\u09ac\u09c3\u09a4\u09cd\u09a4 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\"\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09ac\u09c7\u0997-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\"<\/p>\n

\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997 \u0993 \u09a4\u09cd\u09ac\u09b0\u09a3 (Velocity and acceleration of particles from graphs)<\/b><\/h2>\n

\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09af\u09bc \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 (Distance – time Graphs) \u09b9\u09a4\u09c7 \u09ac\u09c7\u0997 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc:<\/b><\/h3>\n

(i) \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09af\u09bc \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 (\u09b8\u09ae\u09ac\u09c7\u0997\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7):<\/b><\/h4>\n

\u09b8\u09be\u09b0\u09a3\u09bf: \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09df<\/span><\/p>\n\n\n\n\n\n\n\n
\u09b8\u09ae\u09df<\/strong><\/td>\n\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/strong><\/td>\n<\/tr>\n
0<\/td>\n0<\/td>\n<\/tr>\n
3<\/td>\n6<\/td>\n<\/tr>\n
6<\/td>\n12<\/td>\n<\/tr>\n
9<\/td>\n18<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

\"\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\"<\/p>\n

\u09b8\u09ae\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u098f\u0995\u0987 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09ac\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09b8\u09ae\u09af\u09bc \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 \u09ae\u09c2\u09b2\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u098f\u0995\u099f\u09bf \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be <\/span>OP<\/span> \u09b9\u09af\u09bc\u0964<\/span><\/p>\nO P \\text { \u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 }=\\frac{18-0}{9-0}=2 \\mathrm{~km} \/ \\min =\\text { \u09ac\u09c7\u0997\u0964 }<\/span>\n

<\/h4>\n

(ii) \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8-\u09b8\u09ae\u09af\u09bc \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 (\u0985\u09b8\u09ae \u09ac\u09c7\u0997\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7):<\/b><\/h4>\n

\u0985\u09b8\u09ae \u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u098f\u0995\u0987 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7 \u09a8\u09be\u0964 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>(s)<\/span><\/span> \u0993 \u09b8\u09ae\u09af\u09bc <\/span>(t)<\/span><\/span> \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0997\u09a4\u09bf\u09aa\u09a5 <\/span>s=f(t)<\/span><\/span> \u098f\u0995\u099f\u09bf \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be \u09b9\u09af\u09bc\u0964 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09ac\u09c7\u0997 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc\u09c7 <\/span>s=f(t)<\/span><\/span>\u00a0\u098f\u09b0 \u0990 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09a2\u09be\u09b2 \u09a8\u09bf\u09b2\u09c7 \u09ac\u09c7\u0997 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964<\/span><\/p>\n

\"\u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0<\/p>\n

\"\u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0<\/p>\n

\u098f\u09b0\u09c2\u09aa \u09ac\u0995\u09cd\u09b0\u09b0\u09c7\u0996\u09be\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u09a2\u09be\u09b2 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09ac\u09be \u09b8\u09ae\u09af\u09bc\u09c7 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09ad\u09bf\u09a8\u09cd\u09a8 \u09b9\u09af\u09bc\u0964 \u098f\u0987 \u09a2\u09be\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u0990 \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09b8\u09ae \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n\\text { \u099a\u09bf\u09a4\u09cd\u09b0 \u0985\u09a8\u09af\u09be\u09af\u09bc\u09c0, } P \\text { \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09c7\u0997 }=\\frac{A B}{C B}<\/span>\n

<\/h3>\n

\u09ac\u09c7\u0997 \u09b8\u09ae\u09af\u09bc \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0 (Velocity-time Graphs) \u09b9\u09a4\u09c7 \u09ac\u09c7\u0997, \u09a4\u09cd\u09ac\u09b0\u09a3 \u0993 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc<\/b><\/h3>\n

\"\u09ac\u09c7\u0997-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0-\u09e7\"<\/p>\n

\"\u09ac\u09c7\u0997-\u09b8\u09ae\u09df-\u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0-\u09e8\"<\/p>\n

\u099a\u09bf\u09a4\u09cd\u09b0-\u09e7 \u098f <\/span>v=u+f t<\/span><\/span> \u098f\u09b0 \u09b2\u09c7\u0996\u099a\u09bf\u09a4\u09cd\u09b0\u09c7 <\/span>A B<\/span><\/span> \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u0964 <\/span>A B<\/span>, v<\/span>-\u0985\u0995\u09cd\u09b7\u0995\u09c7 <\/span>A<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u0964 <\/span>B<\/span><\/span> \u09b9\u09a4\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b2\u09ae\u09cd\u09ac <\/span>t<\/span><\/span> \u0985\u0995\u09cd\u09b7\u0995\u09c7 <\/span>D<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u09ac\u0982 <\/span>A<\/span><\/span> \u09b9\u09a4\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b2\u09ae\u09cd\u09ac <\/span>B D<\/span><\/span> \u0995\u09c7 <\/span>C<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u099b\u09c7\u09a6 \u0995\u09b0\u09c7\u0964<\/span><\/p>\n

\u2234<\/span> \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0986\u09a6\u09bf\u09ac\u09c7\u0997 <\/span>u=O A<\/span>,<\/span> \u09b8\u09ae\u09df <\/span>t=O D<\/span>,\u00a0\u00a0t<\/span><\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09b0 \u09ac\u09c7\u0997 <\/span>v=B C<\/span> ,<\/span> \u09a4\u09cd\u09ac\u09b0\u09a3 f=\\frac{B C}{A C}<\/span><\/span>\u00a0<\/span><\/p>\n

\u098f\u0996\u09a8, <\/span>O A B D<\/span><\/span> \u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09df\u09be\u09ae\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 <\/span><\/p>\n

=\\frac{1}{2}(A O+B D) \\times O D=\\frac{1}{2}(A O+C D+B C) \\times O D<\/span><\/span><\/p>\n=\\frac{1}{2}(u+u+f . A C) \\times t=\\frac{1}{2}(2 u+f: t) \\times t<\/span>\n=u t+\\frac{1}{2} f t^{2}=s<\/span>\n

\\therefore t<\/span><\/span> \u09b8\u09ae\u09df\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac, s=u t+\\frac{1}{2} f t^{2}=O A B D<\/span><\/span>\u00a0\u099f\u09cd\u09b0\u09be\u09aa\u09bf\u099c\u09bf\u09df\u09be\u09ae\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u0964<\/span><\/p>\n

\u099a\u09bf\u09a4\u09cd\u09b0-\u09e8 \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

\u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7: <\/b>\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>=OA<\/span> \u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 <\/span>=\\frac{30}{20}=\\frac{3}{2} \\mathrm{~ms}^{-2}<\/span><\/span><\/p>\n

\u09b8\u09ae\u09ac\u09c7\u0997\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7: <\/b>\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>=A B<\/span><\/span> \u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 <\/span>=0<\/span><\/p>\n

\u09b8\u09ae\u09ae\u09a8\u09cd\u09a6\u09a8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7: <\/b>\u09a4\u09cd\u09ac\u09b0\u09a3 <\/span>=B C<\/span><\/span> \u09b0\u09c7\u0996\u09be\u09b0 \u09a2\u09be\u09b2 =\\frac{-10}{10}=-1 \\mathrm{~ms}^{-2}<\/span><\/span><\/p>\n

\u0985\u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7: <\/b>P<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 =\\frac{20}{30}=\\frac{2}{3} \\mathrm{~ms}^{-2}<\/span><\/span><\/p>\n

\u0985\u09b8\u09ae \u09ae\u09a8\u09cd\u09a6\u09a8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7: <\/b>Q<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 =\\frac{-20}{30}=-\\frac{2}{3} m s^{-2}<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0997\u09a1\u09bc \u09ac\u09c7\u0997 (Average Velocity) \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u099a\u09b2\u09ae\u09be\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 \u0986\u09a6\u09bf\u09ac\u09c7\u0997\u09c7 \u098f\u09ac\u0982 \u09b8\u09c1\u09b7\u09ae \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u09af\u09be\u09a4\u09cd\u09b0\u09be \u0995\u09b0\u09c7 \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u09ac\u09c7\u0997 \u0985\u09b0\u09cd\u099c\u09a8 \u0995\u09b0\u09c7\u0964 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987, \u098f\u09ac\u0982 N.B.: \u00a0 \u09b8\u09ae\u09a4\u09cd\u09ac\u09b0\u09a3\u09c7 \u099a\u09b2\u09ae\u09be\u09a8 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac = \u0997\u09a1\u09bc\u09ac\u09c7\u0997 \u09b8\u09ae\u09af\u09bc<\/p>\n

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