ವೇಗ: ಪರಿಷ್ಕರಣೆಗಳ ನಡುವಿನ ವ್ಯತ್ಯಾಸ

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೨೫ ನೇ ಸಾಲು:
===ಸರಾಸರಿ ವೇಗ===
<math>\Delta\boldsymbol{x} : </math> ಒಂದು ಸಣ್ಣ ಸ್ಥಾನಪಲ್ಲಟ, <math>x_೧ -x_೦ </math>,
<math>\Delta\mathit{t} : </math> ಮತ್ತು ಸಣ್ಣ ಸಮಯದ ವ್ಯತ್ಯಾಸ <math>t_೧ -t_೦</math> ಆಗಿದ್ದರೆ, ಆ ಕೂಡಲೇ ಸಂಭವಿಸುವಂತಹ ವೇಗವು,
ಆ ಕೂಡಲೇ ಸಂಭವಿಸುವಂತಹ ವೇಗವು,
:<math>\boldsymbol{\bar{v}} = \frac{\Delta\boldsymbol{x}}{\Delta\mathit{t}} .</math> ಆಗಿರುತ್ತದೆ.
 
:<math>\boldsymbol{\bar{v}} = {1 \over t_1 - t_0 } \int_{t_0}^{t_1} \boldsymbol{v}(t) \ dt ,</math>
 
 
===Instantaneous velocity===
[[File:Velocity vs time graph.svg|thumb|266px|Example of a velocity vs. time graph, and the relationship between velocity '''''v''''' on the y-axis, acceleration '''''a''''' (the three green [[tangent]] lines represent the values for acceleration at different points along the curve) and displacement '''''s''''' (the yellow [[area]] under the curve.)]]
If we consider {{math|'''''v'''''}} as velocity and {{math|'''''x'''''}} as the displacement (change in position) vector, then we can express the (instantaneous) velocity of a particle or object, at any particular time {{math|''t''}}, as the [[derivative]] of the position with respect to time:
 
:<math>\boldsymbol{v} = \lim_{{\Delta t}\to 0} \frac{\Delta \boldsymbol{x}}{\Delta t} = \frac{d\boldsymbol{x}}{d\mathit{t}} .</math>
 
 
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