वेग: Difference between revisions
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पहले सवार की अपेक्षा दूसरे सवार का वेग | पहले सवार की अपेक्षा दूसरे सवार का वेग | ||
<math>\mathbf{V}</math><sub>B</sub><sub>A</sub> = <math>\mathbf{V}</math><sub>B</sub> <math>-</math> <math>\mathbf{V}</math><sub>A</sub> | <math>\mathbf{V}</math><sub>B</sub><sub>A</sub> = <math>\mathbf{V}</math><sub>B</sub> <math>-</math> <math>\mathbf{V}</math><sub>A</sub> | ||
तथा, दूसरे सवार की अपेक्षा पहले सवार का वेग | तथा, दूसरे सवार की अपेक्षा पहले सवार का वेग | ||
<math>\mathbf{V}</math><sub>A</sub><sub>B</sub> = <math>\mathbf{V}</math><sub>A</sub> <math>-</math> <math>\mathbf{V}</math><sub>B</sub> | <math>\mathbf{V}</math><sub>A</sub><sub>B</sub> = <math>\mathbf{V}</math><sub>A</sub> <math>-</math> <math>\mathbf{V}</math><sub>B</sub> | ||
*'''विपरीत दिशा में'''- जब दोनों सवार एक–दूसरे के विपरीत दिशा में गतिमान हों, तो ऐसी स्थित में | *'''विपरीत दिशा में'''- जब दोनों सवार एक–दूसरे के विपरीत दिशा में गतिमान हों, तो ऐसी स्थित में | ||
पहले सवार की अपेक्षा दूसरे सवार का वेग | पहले सवार की अपेक्षा दूसरे सवार का वेग | ||
<math>\mathbf{V}</math><sub>B</sub><sub>A</sub> = <math>\mathbf{V}</math><sub>B</sub> <math>-</math> (<math>-</math> <math>\mathbf{V}</math><sub>A</sub>) | <math>\mathbf{V}</math><sub>B</sub><sub>A</sub> = <math>\mathbf{V}</math><sub>B</sub> <math>-</math> (<math>-</math> <math>\mathbf{V}</math><sub>A</sub>) | ||
<math>\mathbf{V}</math><sub>B</sub><sub>A</sub> = <math>\mathbf{V}</math><sub>B</sub> <math>+ | <math>\mathbf{V}</math><sub>B</sub><sub>A</sub> = <math>\mathbf{V}</math><sub>B</sub> <math>+</math> <math>\mathbf{V}</math><sub>A</sub> | ||
तथा, दूसरे सवार की अपेक्षा पहले सवार का वेग | तथा, दूसरे सवार की अपेक्षा पहले सवार का वेग | ||
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<math>\mathbf{V}</math><sub>A</sub><sub>B</sub> = <math>\mathbf{V}</math><sub>A</sub> <math>-</math> (<math>-</math><math>\mathbf{V}</math><sub>B</sub>) | <math>\mathbf{V}</math><sub>A</sub><sub>B</sub> = <math>\mathbf{V}</math><sub>A</sub> <math>-</math> (<math>-</math><math>\mathbf{V}</math><sub>B</sub>) | ||
<math>\mathbf{V}</math><sub>A</sub><sub>B</sub> = math>\mathbf{V}</math><sub>A</sub> <math>+</math> <math>\mathbf{V}</math><sub>B</sub> | <math>\mathbf{V}</math><sub>A</sub><sub>B</sub> = <math>\mathbf{V}</math><sub>A</sub> <math>+</math> <math>\mathbf{V}</math><sub>B</sub> | ||
<math>\mathbf{V}- + </math><sub>A</sub> | |||
{{लेख प्रगति | {{लेख प्रगति | ||
|आधार=आधार1 | |आधार=आधार1 | ||
Revision as of 13:13, 8 August 2010
गतिशील वस्तु के विस्थापन की दर अर्थात् एक सेकेण्ड में हुए विस्थापन को वस्तु का वेग कहते हैं।
वेग = विस्थापन/समय
वेग एक सदिश राशि है। इसका SI मात्रक मीटर/सेकेण्ड होता है। वस्तु का वेग धनात्मक व ऋणात्मक दोनों ही हो सकता है, जबकि चाल सदैव धनात्मक होती है। वेग बताते समय उसकी दिशा भी अवश्य ही बताई जाती है। जब कोई वस्तु एक वृत्तीय मार्ग पर एक समान चाल से चल रही हो तो उसका वेग हर बिन्दु पर बदल जाता है, क्योंकि वेग कि दिशा बदल रही है। वृत्त के किसी बिन्दु पर खींची गई स्पर्श रेखा की दिशा ही उस बिन्दु पर वेग की दिशा होती है।
आपेक्षिक वेग
जब वस्तु गतिमान हों, तो एक की अपेक्षा दूसरे का वेग आपेक्षिक वेग कहलाता है। वस्तु Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {A}} का Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {B}} के सापेक्ष वेग वह वेग है, जिससे Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {B}} से देखने पर वस्तु Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {A}} चलती हुई प्रतीत होती है।
उदाहरण:-
- माना कि दो साइकिल सवार क्रमशः Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A और Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B के वेग से चल रहे हैं।
- समान दिशा में- जब दोनों सवार एक हि दिशा में गतिमान हों, ऐसी स्थिति में
पहले सवार की अपेक्षा दूसरे सवार का वेग
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} BA = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A
तथा, दूसरे सवार की अपेक्षा पहले सवार का वेग
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} AB = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B
- विपरीत दिशा में- जब दोनों सवार एक–दूसरे के विपरीत दिशा में गतिमान हों, तो ऐसी स्थित में
पहले सवार की अपेक्षा दूसरे सवार का वेग
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} BA = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): - (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A)
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} BA = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): + Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A
तथा, दूसरे सवार की अपेक्षा पहले सवार का वेग
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} AB = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): - (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B)
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} AB = Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} A Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): + Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}} B
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\mathbf {V}}-+ A
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