Instantaneous Velocity Formula |
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\( v(t) \;=\; \lim_{ \Delta t \rightarrow 0 } \dfrac{ dx }{ d t }\) (Instantaneous Velocity) \( dx \;=\; v(t) \cdot d t \) \( d t \;=\; \dfrac{ dx }{ v(t) }\) |
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| Symbol | English | Metric |
| \( v(t) \) = instantaneous velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( d x \) = Infinitesimally Small Change in Position | \(ft\) | \(m\) |
| \( d t \) = Infinitesimally Small Change in Time | \(sec\) | \(s\) |
Instantaneous velocity, abbreviated as \( v_{ins} \), is the velocity of an object at a specific moment in time. It describes both the speed and direction of motion at that exact instant, rather than over a period of time like average velocity. Mathematically, it is defined as the limit of the average velocity as the time interval approaches zero, where \( d x \) is an infinitesimally small displacement and \( d t \) is an infinitesimally small time interval. Instantaneous velocity is crucial in understanding how an object’s motion changes continuously, especially when acceleration is present.
