Average Acceleration

on . Posted in Classical Mechanics

Average acceleration, abbreviated as \( \bar {a} \), is the change of velocity over an elapsed amount of time.  Whereas, instantaneous accleration is the change of velocity at a specific point in time.  As an example, if a vehicle is initially traveling at 100 feet per second and slows down to 50 feet per second over 60 seconds, the average acceleration over 60 seconds is - 8.3 ft per second.  The equation and calulation for average acceleration is shown below. 


Average acceleration formulas

\(\large{ \bar {a} = \frac{ \Delta v }{ \Delta t }  }\) 

\(\large{ \bar {a} = \frac{ v_f \;-\; v_i }{ t_f \;-\; t_i }   }\) 

Symbol English Metric
\(\large{ \bar {a} }\) = average acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)
\(\large{ \Delta t }\) = time change \(\large{sec}\) \(\large{s}\)
\(\large{ t_f }\) = final time \(\large{sec}\) \(\large{s}\)
\(\large{ t_i }\) = initial time  \(\large{sec}\)  \(\large{s}\)
\(\large{ \Delta v }\) = velocity change \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ v_f }\) = final velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)
\(\large{ v_i }\) = initial velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{s}}\)


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Tags: Acceleration Equations