Instantaneous Acceleration

Instantaneous acceleration, abbreviated as \(a_i\), is the acceleration at a particular moment in time along its path.  Because acceleration is measured of the rate of change in velocity, the derivative of the velocity curve needs to be known.  Additionally, the position curve could be known and the second derivative could be applied to that to find the acceleration. 

 

Instantaneous Acceleration formula
\( a_i =  dv \;/\; dt  \)     (Instantaneous Acceleration) \( dv =  a_i \; dt   \) \( dt =  dv \;/\; a_i   \)
Symbol	English	Metric
\( a_i \) = instantaneous acceleration	\(ft / sec^2\)	\(m / s^2\)
\( dt \) = time derivative	\(sec\)	\(s\)
\( dv \) = velocity derivative	\(ft / sec\)	\(m / s\)