Instantaneous Acceleration Formula |
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\( a(t) \;=\; \lim_{ \Delta t \rightarrow 0 } \dfrac{ dv }{ dt }\) (Instantaneous Acceleration) \( dv \;=\; a(t) \cdot dt \) \( dt \;=\; \dfrac{ dv }{ a(t) }\) |
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| Symbol | English | Metric |
| \( a(t) \) = Instantaneous Acceleration | \(ft \;/\; sec^2\) | \(m \;/\; s^2\) |
| \( dv \) = Infinitesimally Small Change in Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( dt \) = Infinitesimally Small Change in Time | \(sec\) | \(s\) |
Instantaneous acceleration, abbreviated as \(a(t)\), is the acceleration of an object at a specific moment in time, rather than over a longer interval. It describes how quickly the object’s velocity is changing at that exact instant. In calculus terms, instantaneous acceleration is defined as the derivative of velocity with respect to time, or equivalently the second derivative of position with respect to time. This makes it a very precise measurement of motion, capturing even very small and rapid changes in velocity. Other words, if you imagine looking at an object’s motion through a microscope of time, instantaneous acceleration tells you how fast its speed and direction are changing at that microscopic moment.
- See Article - Acceleration Conversion
